Paper: arXiv 2407.03431

Authors: Marcelo Righi

Abstract

We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the optimization problem as a convex and monotone map per se. We also derive results for optimality and indifference pricing conditions. We also explore particular examples inside our setup.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework for optimal hedging under variational preferences and convex risk measures, featuring detailed dual representation proofs and sub-differential derivations. However, it is a purely theoretical note that completely lacks empirical data, backtesting, or quantitative simulations.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Hedging & Indifference Pricing with Variational Preferences] --> B[Inputs: Convex Risk Measures & Utility Functions]
    B --> C[Establish Dual Representation of Risk-Utility Compositions]
    C --> D[Analyze Convex & Monotone Optimization Mapping]
    D --> E[Derive Optimality & Indifference Pricing Conditions]
    E --> F[Outcomes: Theoretical Framework & Specific Model Examples]

Cited References (819)

  1. Risk measure pricing and hedging in incomplete markets (2006)
  2. Robust Risk-Aware Option Hedging — → 2303.15216
  3. Risk measures and robust optimization problems (2006)
  4. Convex hedging in incomplete markets (2007)
  5. Efficient hedging with coherent risk measure (2004)
  6. On RVaR-based optimal partial hedging (2022)
  7. Optimal static-dynamic hedges for exotic options under convex risk measures (2009)
  8. Minimizing CVaR in global dynamic hedging with transaction costs (2016)
and 811 more
  1. Efficient hedging: cost versus shortfall risk (2000)
  2. VaR-based optimal partial hedging (2013)
  3. Pricing and hedging European options with discrete-time coherent risk (2007)
  4. Duality formulas for robust pricing and hedging in discrete time (2017)
  5. Deep hedging (2019)
  6. Inf-convolution of risk measures and optimal risk transfer (2005)
  7. Extending pricing rules with general risk functions (2010)
  8. Hedging, Pareto optimality, and good deals (2013)
  9. Optimization of risk measures (2006)
  10. Optimizing distortion riskmetrics with distributional uncertainty (2022) — link
  11. Portfolio optimization within a Wasserstein ball (2023)
  12. Inf-convolution, optimal allocations, and model uncertainty for tail risk measures (2022)
  13. Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization (2018)
  14. Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations (2018)
  15. Upper bounds for strictly concave distortion risk measures on moment spaces (2018)
  16. Equivalent distortion risk measures on moment spaces (2019)
  17. Sharing the value-at-risk under distributional ambiguity (2021)
  18. Distributionally robust optimization under distorted expectations (2023)
  19. Distributionally robust mean-variance portfolio selection with Wasserstein distances (2022)
  20. Robust distortion risk measures (2023) — link
  21. Computational aspects of robust optimized certainty equivalents and option pricing (2020)
  22. Set-valued analysis (2009)
  23. Variational Analysis (2009)
  24. Uncertainty Propagation and Dynamic Robust Risk Measures — → 2308.12856
  25. Valadier-like Formulas for the Supremum Function. II: The Compactly Indexed Case (2019)
  26. An extreme worst-case risk measure by expectile (2024)
  27. Monetary utility functions (2012)
  28. Robust Hedging GANs — → 2307.02310
  29. On convex risk measures on Lp-spaces (2009)
  30. Quantitative risk management: Concepts, techniques and tools (2015)
  31. THE CANONICAL MODEL SPACE FOR LAW-INVARIANT CONVEX RISK MEASURES IS L1 (2012)
  32. Set risk measures — → 2407.18687
  33. Extreme-Case Distortion Risk Measures: A Unification and Generalization of Closed-Form Solutions (2023) — link
  34. Preference robust distortion risk measure and its application (2023) — link
  35. Ambiguity aversion, robustness, and the variational representation of preferences (2006)
  36. Hedging with small uncertainty aversion (2017)
  37. Convex analysis in general vector spaces (2002)
  38. Convex analysis and variational problems (1999)
  39. Robustifying convex risk measures for linear portfolios: A nonparametric approach (2014)
  40. AN OLD-NEW CONCEPT OF CONVEX RISK MEASURES: THE OPTIMIZED CERTAINTY EQUIVALENT (2007) — link
  41. Topics in optimal transportation (2021)
  42. Distortion risk measure under parametric ambiguity (2023)
  43. Extremal cases of distortion risk measures with partial information — → 2404.13637
  44. Worst-cases of distortion riskmetrics and weighted entropy with partial information — → 2405.19075
  45. Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty — → 2304.04396
  46. A note on continuity and consistency of measures of risk and variability — → 2405.09766
  47. The pricing of options and corporate liabilities (1973)
  48. Theory of rational option pricing (1973)
  49. Robustness (2008)
  50. Robust convex risk measures — → 2406.12999
  51. Quantile Uncertainty and Value-at-Risk Model Risk (2012)
  52. Model Risk and Uncertainty - Illustrated with Examples from Mathematical Finance (2014)
  53. Assessing financial model risk (2015) — link
  54. Measure Theory (2006) — link
  55. Risk models-at-risk (2014)
  56. Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation (1982)
  57. A test for normality of observations and regression residuals (1987)
  58. Quantifying market risk with Value-at-Risk or Expected Shortfall? C onsequences for capital requirements and model risk (2016)
  59. Model risk and capital reserves (2010)
  60. Quantifying model risk (2014)
  61. Testing for unit roots in autoregressive-moving average models of unknown order (1984)
  62. A systematic design for coping with model risk (2011) — link
  63. Measuring market risk (2007)
  64. On the necessity of five risk measures (2012)
  65. Forecasting VaR and ES of stock index portfolio: A Vine copula method (2014)
  66. On the coherence of expected shortfall (2002) — link
  67. Generalized autoregressive conditional heteroskedasticity (1986)
  68. Overview of the amendment to the capital accord to incorporate market risks (1996)
  69. Fundamental review of the trading book: A revised market risk framework (2013) — link
  70. Portfolio selection (1952)
  71. Model Risk of Risk Models (2016)
  72. Enterprise risk management: coping with model risk in a large bank (2010)
  73. Three Cheers: Why the Basel Committee’s market risk multiplication factor is fully justified (1997)
  74. A new approach to assessing model risk in high dimensions (2015)
  75. Model uncertainty and its impact on the pricing of derivative instruments (2006)
  76. Statistics and quantitative risk management for banking and insurance (2014)
  77. Measuring model risk (2008)
  78. An Economic Evaluation of Model Risk in Long-term Asset Allocations (2013)
  79. Learning by failing: a simple VaR buffer (2013)
  80. Techniques for verifying the accuracy of risk measurement models (1995)
  81. Evaluating interval forecasts (1998)
  82. Testing density forecasts, with applications to risk management (2001)
  83. On conditional risk estimation considering model risk (2016)
  84. Uncertainty and profit (1921)
  85. Capturing parameter risk with convex risk measures (2013)
  86. Model uncertainty and its impact on derivative pricing (2010)
  87. Implications of parameter uncertainty on option prices (2010)
  88. Parametric model risk and power plant valuation (2016)
  89. An introduction to Bartlett correction and bias reduction (2014)
  90. Bias of a Value-at-Risk estimator (2004)
  91. Quantifying and correcting the bias in estimated risk measures (2007)
  92. Model uncertainty and liquidity (2009)
  93. Intertemporal asset pricing under Knightian uncertainty (1994)
  94. A methodology for assessing model risk and its application to the implied volatility function model (2002)
  95. Model uncertainty in risk capital measurement (2016)
  96. Parameter uncertainty and residual estimation risk (2015)
  97. Interval forecasts and parameter uncertainty (2006)
  98. Reducing model risk via positive and negative dependence assumptions (2015)
  99. Model risk of contingent claims (2016)
  100. Supervisory guidance on model risk management (2011) — link
  101. Robust capital requirements with model risk (2015)
  102. Coherent Measures of Risk (1999)
  103. Generalized deviations in risk analysis (2006)
  104. Supervisory Guidance on Model Risk Management (2011)
  105. Applying the Requirement for Conservatism to the Parameters in the Advanced Approaches (2013)
  106. Model risk (1996)
  107. An investigation of model risk in a market with jumps and stochastic volatility (2016)
  108. Model risk of the implied GARCH -normal model (2014)
  109. Shortfall deviation risk: an alternative for risk measurement (2016)
  110. Measuring distribution model risk (2016)
  111. Value at Risk : the new benchmark for managing financial risk (2006)
  112. Robust valuation and risk measurement under model uncertainty (2014) — link
  113. Coping with model risk (2000)
  114. The role of model risk in extreme value theory for capital adequacy (2016)
  115. Statistical analysis of model risk concerning temperature residuals and its impact on pricing weather derivatives (2012)
  116. Quantile of a mixture with application to model risk assessment (2015)
  117. Model uncertainty and VaR aggregation (2013)
  118. Robust and practical estimation for measures of tail risk (2014)
  119. Model risk and option hedging (2004)
  120. Model risk in portfolio optimization (2014)
  121. Data-generating process uncertainty: What difference does it make in portfolio decisions? (2004)
  122. Bayes-Stein estimation for portfolio analysis (1986)
  123. Optimal portfolio choice with parameter uncertainty (2007)
  124. A review of different perspectives on uncertainty and risk and an alternative modeling paradigm (2009)
  125. Models and model uncertainty in the context of risk analysis (2003)
  126. Revisions to the Basel II market risk framework (2009) — link
  127. Loss-Deviation risk measures (2015) — link
  128. Estimation bias in the first-order autoregressive model and its impact on predictions and prediction intervals (2009)
  129. Adjusted empirical likelihood for value at risk and expected shortfall (2017)
  130. Coherence and elicitability (2016)
  131. Model risk: A conceptual framework for risk measurement and hedging (2004) — [link](https://ssrn.com/abstract=493482 or http://dx.doi.org/10.2139/ssrn.493482)
  132. About the impact of model risk on capital reserves: a quantitative analysis. (2015)
  133. Time Series Simulation with Randomized Quasi-Monte Carlo Methods : an Application to Value at Risk and Expected Shortfall (2017)
  134. Model risk adjusted hedge ratios (2009)
  135. Measures of model uncertainty and calibrated option bounds (2009)
  136. Applying hedging strategies to estimate model risk and provision calculation (2013)
  137. Incorporating model uncertainty into optimal insurance contract design (2017)
  138. Systematic stress tests with entropic plausibility constraints (2013)
  139. Risk aggregation with dependence uncertainty (2014)
  140. Sharp bounds on the expected shortfall for a sum of dependent random variables (2013)
  141. How robust is the value-at-risk of credit risk portfolios? (2015)
  142. Forecasting credit card portfolio losses in the Great Recession: a study in model risk (2015)
  143. A normalized measure of model risk (2010) — link
  144. Why risk is so hard to measure (2016)
  145. An academic response to Basel 3.5 (2014)
  146. Aggregation-robustness and model uncertainty of regulatory risk measures (2015)
  147. Accurate value-at-risk forecasting based on the normal-GARCH model (2006)
  148. Efficient Monte Carlo methods for convex risk measures in portfolio credit risk models (2007)
  149. Worst case model risk management (2002)
  150. Quantile regression forecasts of inflation under model uncertainty (2017)
  151. Model risk and its control (2000)
  152. Model risk in backtesting risk measures (2014)
  153. External risk measures and Basel accords (2013)
  154. Estimating quantile sensitivities (2009)
  155. Simulating sensitivities of conditional value at risk (2009)
  156. Worst-case robust decisions for multi-period mean–variance portfolio optimization (2007)
  157. Worst-case robust Omega ratio (2014)
  158. Risk management lessons from the credit crisis (2009)
  159. Testing the null hypothesis of stationarity against the alternative of a unit root (1992)
  160. Model risk and regulatory capital (2002)
  161. Modifying goodness-of-fit indicators to incorporate both measurement and model uncertainty in model calibration and validation (2010)
  162. Model Risk in Financial Markets: From Financial Engineering to Risk Management (2015)
  163. General Properties of Backtestable Statistics (2017) — link
  164. On the measurement of economic tail risk (2016)
  165. Expected shortfall or median shortfall (2014)
  166. Failure probability under parameter uncertainty (2011)
  167. Comparative and qualitative robustness for law-invariant risk measures (2014)
  168. Qualitative and infinitesimal robustness of tail-dependent statistical functionals (2012)
  169. Robustness and sensitivity analysis of risk measurement procedures (2010)
  170. Using B ayesian Statistics to Model Uncertainty in Mixture Models: A Sensitivity Analysis of Priors (2017)
  171. Model risk and discretisation of locally risk-minimising strategies (2017)
  172. Bayesian risk management: a guide to model risk and sequential learning in financial markets (2015)
  173. Volatility options: Hedging effectiveness, pricing, and model error (2006)
  174. On the properties of the Lambda value at risk: robustness, elicitability and consistency (2017)
  175. A new loss function for multi-response optimization with model parameter uncertainty and implementation errors (2017)
  176. The opportunity cost of mean–variance choice under estimation risk (2014)
  177. Hedging variance options on continuous semimartingales (2010)
  178. Risk minimization in stochastic volatility models: Model risk and empirical performance (2009)
  179. Bid-Ask Spread for Exotic Options under Conic Finance (2015)
  180. Stock return predictability and model uncertainty (2002)
  181. Model averaging in economics: An overview (2015)
  182. Model uncertainty effect on asset prices (2017)
  183. Portfolio Capital Flows in T hailand: A B ayesian Model Averaging Approach (2014)
  184. Putting order in risk measures (2002)
  185. Static hedging and model risk for barrier options (2006)
  186. Model Risk in Option Pricing (2008) — link
  187. A Novel Approach to Quantification of Model Risk for Practitionners (2017) — link
  188. Maximum Entropy Principle with General Deviation Measures (2009)
  189. The natural Banach space for version independent risk measures (2013)
  190. Infinite Dimensional Analysis (2006)
  191. Diversification-consistent data envelopment analysis with general deviation measures (2013)
  192. Optimality conditions in portfolio analysis with general deviation measures (2006)
  193. Deviation Measures on Banach Spaces and Applications (2013)
  194. The level and quality of Value-at-Risk disclosure by commercial banks (2010)
  195. Risk tuning with generalized linear regression (2008)
  196. Law invariant risk measures have the Fatou property (2006)
  197. The axiomatic approach to risk measures for capital determination (2015)
  198. Stochastic finance: an introduction in discrete time (2016)
  199. Law invariant convex risk measures (2005)
  200. Teoria de Medidas de Risco: Uma Revis ~a o Abrangente (Risk Measures Theory: A Comprehensive Survey) (2014)
  201. Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks (2017)
  202. Closed spaces induced by deviation measures (2017)
  203. A composition between risk and deviation measures (2019)
  204. The concept of comonotonicity in actuarial science and finance: theory (2002)
  205. OCC Bulletin, Model Validation, 16 (2000)
  206. A risk measure that optimally balances capital determination errors (2017) — link
  207. A simulation comparison of risk measures for portfolio optimization (2018)
  208. Model averaging in risk management with an application to futures markets (2009)
  209. Introduction to statistical quality control (2007)
  210. Forecasting realized volatility in a changing world: A dynamic model averaging approach (2016)
  211. The combination of forecasts (1969)
  212. Forecast accuracy and economic gains from B ayesian model averaging using time-varying weights (2010)
  213. A comparison of Expected Shortfall estimation models (2015)
  214. Large deviations for risk measures in finite mixture models (2017)
  215. Estimation-Adjusted VaR (2013)
  216. Predicting short-term interest rates using B ayesian model averaging: Evidence from weekly and high frequency data (2013)
  217. Forecasting realized volatility: a B ayesian model-averaging approach (2009)
  218. Value-at-risk for long and short trading positions (2003)
  219. Elicitability and backtesting: Perspectives for banking regulation (2017)
  220. Measuring Model Risk in Financial Risk Management and Pricing (2018) — link
  221. Modeling Dependence Between Financial Returns Using Pair-Copula Constructions (2011)
  222. Spectral measures of risk: A coherent representation of subjective risk aversion (2002)
  223. Construction of multivariate distributions: a review of some recent results (2008)
  224. The use of GARCH models in VaR estimation (2004)
  225. Comparing simulation models for market risk stress testing (2011) — link
  226. On the isolated impact of copulas on risk measurement: Asimulation study (2016) — link
  227. The efficiency of the estimators of the parameters in GARCH processes (2004)
  228. Evaluating value-at-risk models with desk-level data (2011)
  229. A comparison of extreme value theory approaches for determining value at risk (2005)
  230. Ten things you should know about the dynamic conditional correlation representation (2013)
  231. Copula-based nonlinear quantile autoregression (2009) — link
  232. Copula methods in finance (2004)
  233. Elements of financial risk management (2012)
  234. Selection of vine copulas (2013)
  235. Financial risk forecasting: the theory and practice of forecasting market risk with implementation in R and Matlab (2011)
  236. Measuring Market Risk (2005)
  237. An overview of Value at Risk (1997)
  238. Copulas: A Personal View (2009) — link
  239. Strategic long-term financial risks: single risk factors (2005)
  240. Modelling dependence with copulas (2001)
  241. Correlation: pitfalls and alternatives (1999)
  242. Bounds for functions of multivariate risks (2006) — link
  243. Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH (2001)
  244. Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall (2010) — link
  245. The effects of misspecified marginals and copulas on computing the value at risk: a Monte Carlo study (2009)
  246. Dynamic copula modelling for value at risk (2008)
  247. Objective B ayesian analysis for the S tudent-t regression model (2008)
  248. A DARE for VaR (2015)
  249. Downside risk management and VaR-based optimal portfolios for precious metals, oil and stocks (2013) — link
  250. Empirical study of value-at-risk and expected shortfall models with heavy tails (2006)
  251. Measuring the coupled risks: A copula-based \ CVaR\ model (2009) — link
  252. Evaluation of value-at-risk models using historical data (digest summary) (1996)
  253. Construction and sampling of nested A rchimedean copulas (2010)
  254. Sampling A rchimedean copulas (2008)
  255. Nested A rchimedean copulas meet R : The nacopula package (2011)
  256. Estimating value at risk of portfolio by conditional copula- GARCH method (2009)
  257. Small sample properties of GARCH estimates and persistence (2006)
  258. Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data (2008) — link
  259. Multivariate models and multivariate dependence concepts (1997)
  260. Asymmetry in tail dependence in equity portfolios (2016)
  261. Financial Risk Manager Handbook (2009)
  262. Measurement of aggregate risk with copulas (2005) — link
  263. Systemic risk among European banks: A copula approach (2016) — link
  264. Assessing value at risk with CARE , the Conditional Autoregressive Expectile models (2009) — link
  265. Dependence modeling: vine copula handbook (2011)
  266. Evaluating the accuracy of value-at-risk forecasts: New multilevel tests (2014) — link
  267. The comovement between output and prices: Evidence from a dynamic conditional correlation GARCH model (2006)
  268. Extreme correlation of international equity markets (2001)
  269. The asymptotic distribution of extreme stock market returns (1996)
  270. Canonical vine copulas in the context of modern portfolio management: Are they worth it? (2013)
  271. Parametric Value-at-Risk analysis: Evidence from stock indices (2012) — link
  272. The variation of certain speculative prices (1963)
  273. Value at risk models in finance (2001) — link
  274. A comparison of some univariate models for value-at-risk and expected shortfall (2007) — link
  275. Sampling nested Archimedean copulas (2008)
  276. Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach (2000)
  277. Assessing the bias of maximum likelihood estimates of contaminated GARCH models (2000)
  278. Measuring financial risks with copulas (2004)
  279. An Introduction to Copulas (2006)
  280. Measuring financial risk: comparison of alternative procedures to estimate VaR and ES (2008)
  281. Using conditional copula to estimate value at risk (2006)
  282. An empirical investigation of the rank correlation between different risk measures (2004)
  283. Measuring systemic risk using vine-copula (2016) — link
  284. Analyzing the dependence structure of various sectors in the Brazilian market: A Pair Copula Construction approach (2013) — link
  285. Pair Copula Construction based Expected Shortfall estimation (2013)
  286. Hierarchies of Archimedean copulas (2010)
  287. Fonctions de r'epartition 'a n dimensions et leurs marges (1959)
  288. Estimating Value at Risk and Expected Shortfall Using Expectiles (2008) — link
  289. A multivariate GARCH model with time-varying correlations (2000)
  290. Sampling from Archimedean copulas (2004)
  291. Capturing Tail Risks Beyond VaR (2012) — link
  292. On the validity of Value-at-Risk : comparative analyses with Expected Shortfall (2002)
  293. Marginal or copula: which one is critical? (2013)
  294. Backtesting Expected Shortfall (2014)
  295. Developing a stress testing framework based on market risk models (2008) — link
  296. On elicitable risk measures (2015)
  297. Generalized quantiles as risk measures (2014)
  298. Generalized autoregressive conditional heteroskedasticity (1986)
  299. Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50 (2013)
  300. Testing and comparing Value-at-Risk measures (2001) — link
  301. Selection of vine copulas (2013)
  302. A remark on the structure of expectiles (2013) — link
  303. Strategic long-term financial risks: single risk factors (2005)
  304. Modelling dependence with copulas (2001)
  305. Correlation: pitfalls and alternatives (1999)
  306. The effects of misspecified marginals and copulas on computing the value at risk: a Monte Carlo study (2009)
  307. Dynamic copula modelling for value at risk (2008)
  308. Higher order elicitability and Osband’s principle (2016)
  309. Construction and sampling of nested A rchimedean copulas (2010)
  310. Sampling A rchimedean copulas (2008)
  311. Value at Risk : the new benchmark for managing financial risk (2006)
  312. Financial Risk Manager Handbook (2009)
  313. External risk measures and Basel accords (2013)
  314. On law invariant coherent risk measures (2001)
  315. The hidden dangers of historical simulation (2006)
  316. Analyzing the dependence structure of various sectors in the Brazilian market: A Pair Copula Construction approach (2013) — link
  317. Pair Copula Construction based Expected Shortfall estimation (2013)
  318. Copula- GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy (2013)
  319. Value-at-risk versus expected shortfall: A practical perspective (2005) — link
  320. Model risk in VaR estimation: an empirical study (2006)
  321. Shortfall deviation risk: an alternative for risk measurement (2016)
  322. Pair-copula constructions of multiple dependence (2009)
  323. A robust VaR model under different time periods and weighting schemes (2007)
  324. Risk management with expectiles (2017)
  325. Selection of vine copulas (2013)
  326. Strategic long-term financial risks: single risk factors (2005)
  327. Correlation: pitfalls and alternatives (1999)
  328. The effects of misspecified marginals and copulas on computing the value at risk: a Monte Carlo study (2009)
  329. Dynamic copula modelling for value at risk (2008)
  330. Value at Risk : the new benchmark for managing financial risk (2006)
  331. Financial Risk Manager Handbook (2009)
  332. Improved estimation of portfolio value-at-risk under copula models with mixed marginals (2006)
  333. Analyzing the dependence structure of various sectors in the Brazilian market: A Pair Copula Construction approach (2013) — link
  334. Pair Copula Construction based Expected Shortfall estimation (2013)
  335. Master funds in portfolio analysis with general deviation measures (2006)
  336. Equilibrium with investors using a diversity of deviation measures (2007)
  337. Inverse portfolio problem with mean-deviation model (2014)
  338. A simple distribution-free test for nonnested model selection (2007)
  339. Analyzing the dependence structure of various sectors in the Brazilian market: A Pair Copula Construction approach (2013) — link
  340. Construction and sampling of nested A rchimedean copulas (2010)
  341. Convex measures of risk and trading constraints (2002)
  342. Correlation: pitfalls and alternatives (1999)
  343. Distribution-free continuous B ayesian belief nets (2005)
  344. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models (2002)
  345. Empirical properties of asset returns: stylized facts and statistical issues (2001)
  346. Estimating hedged portfolio value-at-risk using the conditional copula: An illustration of model risk (2013)
  347. Estimation of risk measures in energy portfolios using modern copula techniques (2014)
  348. Estimation risk in financial risk management (2005)
  349. Extreme risk measures for REIT s: A comparison among alternative methods (2012)
  350. Families of m-variate distributions with given margins and m (m-1)/2 bivariate dependence parameters (1996) — link
  351. Financial risk and heavy tails (2003)
  352. Financial Risk Manager Handbook (2009)
  353. Forecasting Value at Risk and Expected Shortfall based on serial pair-copula constructions (2015) — link
  354. Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence (2013)
  355. Making and evaluating point forecasts (2011)
  356. Model choice and value-at-risk performance (2002)
  357. Modeling Dependence Between Financial Returns Using Pair-Copula Constructions (2011)
  358. Modelling dependence with copulas (2001)
  359. Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model (1990)
  360. Models for construction of multivariate dependence–a comparison study (2009)
  361. Pair Copula Construction based Expected Shortfall estimation (2013)
  362. Probability density decomposition for conditionally dependent random variables modeled by vines (2001)
  363. Risk prediction management and weak form market efficiency in Eurozone financial crisis (2013)
  364. Robust risk measurement and model risk (2014)
  365. Sampling A rchimedean copulas (2008)
  366. Selecting copulas for risk management (2007)
  367. Selection of vine copulas (2013)
  368. Shortfall deviation risk: an alternative for risk measurement (2016)
  369. Strategic long-term financial risks: single risk factors (2005)
  370. The effects of misspecified marginals and copulas on computing the value at risk: a Monte Carlo study (2009)
  371. Unexpected tails in risk measurement: Some international evidence (2014)
  372. Value at Risk : the new benchmark for managing financial risk (2006)
  373. Value-at-risk prediction: A comparison of alternative strategies (2006)
  374. Vines: A new graphical model for dependent random variables (2002)
  375. What is the best risk measure in practice? A comparison of standard measures (2015)
  376. Dependent risk models with A rchimedean copulas: A computational strategy based on common mixtures and applications (2018)
  377. Decision principles derived from risk measures (2010)
  378. Optimal capital allocation principles (2012)
  379. Continuity properties of law-invariant (quasi-)convex risk functions on $L^ \infty $ (2010)
  380. An optimization approach to the dynamic allocation of economic capital (2004)
  381. Natural risk measures (2016)
  382. RISK MEASURES ON P(R) AND VALUE AT RISK WITH PROBABILITY/LOSS FUNCTION (2014)
  383. Comparative and qualitative robustness for law-invariant risk measures (2014)
  384. The fundamental risk quadrangle in risk management, optimization and statistical estimation (2013)
  385. The least squares estimator of random variables under sublinear expectations (2017)
  386. Diversification, protection of liability holders and regulatory arbitrage (2017)
  387. Surplus-Invariant, Law-Invariant, and Positively Homogeneous Acceptance Sets Must be Induced by Value-at-Risk (2017)
  388. A Theory for Measures of Tail Risk (2017)
  389. Risk measures on Orlicz Hearts (2009)
  390. Regulatory arbitrage of risk measures (2016)
  391. Modeling, Measuring and Managing Risk (2007)
  392. Optimal capital allocation based on the Tail Mean–Variance model (2013)
  393. Optimal pricing of a heterogeneous portfolio for a given risk level (2006)
  394. Risk measures based on behavioural economics theory (2018)
  395. Stochastic comparisons of capital allocations with applications (2012)
  396. Model Risk Adjusted Risk Forecasting (2018)
  397. Economic capital allocation derived from risk measures (2003)
  398. Managing economic and virtual economic capital within financial conglomerates (2005)
  399. Optimal pricing for a heterogeneous portfolio for a given risk factor and convex distance measure (2007)
  400. Blame the models (2008)
  401. Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility (2017)
  402. Basel III : a global regulatory framework for more resilient banks and banking systems (2010) — link
  403. Supervisory guidance on model risk management (2011) — link
  404. A theory for combinations of risk measures (2019) — link
  405. Coherent risk measures on general probability spaces (2002)
  406. Revisions to the Basel II market risk framework (2009) — link
  407. Measuring model risk (2013)
  408. Model risk in incomplete markets with jumps (2015)
  409. Numerical comparison of multivariate models to forecasting risk measures (2018)
  410. Measuring the model risk of quadratic risk minimizing hedging strategies with an application to energy markets (2014)
  411. Model risk: concepts, calibration and pricing (2000)
  412. A theory for robust risk measures (2018) — link
  413. Selection of Value-at-Risk models (2003)
  414. Law-invariant risk measures: extension properties and qualitative robustness (2014)
  415. Maxmin expected utility with non-unique prior (1989)
  416. A robust approach for minimization of risk measurement errors (2018) — link
  417. Modelling parameter uncertainty for risk capital calculation (2015)
  418. Model risk measurement under Wasserstein distance (2019) — link
  419. A review of backtesting for value at risk (2018)
  420. Hedging parameter risk (2019)
  421. Backtesting (2010)
  422. A review of backtesting and backtesting procedures (2006)
  423. Modeling, measuring and managing risk (2007)
  424. Package rugarch (2019)
  425. Liquidity spillover in international stock markets through distinct time scales (2014)
  426. Measuring Model Risk in the European Energy Exchange (2018)
  427. Endogenous risk (2003)
  428. Effects of outliers on the identification and estimation of GARCH models (2007)
  429. Risk quantification in turmoil markets (2017)
  430. Liquidity spillover in international stock markets through distinct time scales (2014)
  431. R: A Language and Environment for Statistical Computing (2018) — link
  432. General properties of backtestable statistics (2017)
  433. A Composite Risk Measure Framework for Decision Making Under Uncertainty (2019)
  434. Is the Inf-convolution of Law-invariant Preferences Law-invariant? (2019)
  435. Law invariant convex risk measures for portfolio vectors (2006)
  436. Distributionally robust shortfall risk optimization model and its approximation (2019)
  437. Robust return risk measures (2018)
  438. Computational aspects of robust optimized certainty equivalents and option pricing (2019)
  439. On general minimax theorems (1958)
  440. Scenario-based risk evaluation (2021)
  441. Distributionally Robust Stochastic Programming (2017)
  442. Entropy based risk measures (2020) — link
  443. Dynamic robust Orlicz premia and Haezendonck–Goovaerts risk measures (2021)
  444. Vast portfolio selection with gross-exposure constraints (2012)
  445. The sampling error in estimates of mean-variance efficient portfolio weights (1999)
  446. Estimating the global minimum variance portfolio (2006)
  447. Bayesian Shrinkage of Portfolio Weights (2016)
  448. Extremiles: A new perspective on asymmetric least squares (2019)
  449. Extremile Regression (2021)
  450. Regression Quantiles (1978)
  451. Quantile regression (2005)
  452. Asymmetric least squares estimation and testing (1987)
  453. Sparse and Stable Portfolio Selection With Parameter Uncertainty (2015) — link
  454. Bayes risk, elicitability, and the Expected Shortfall (2021)
  455. On a robust risk measurement approach for capital determination errors minimization (2020)
  456. Risk capital allocation by coherent risk measures based on one-sided moments (2003)
  457. Joint generalized quantile and conditional tail expectation regression for insurance risk analysis (2021)
  458. Financial markets under the global pandemic of COVID-19 (2020)
  459. A hybrid approach to cardinality constraint portfolio selection problem based on nonlinear neural network and genetic algorithm (2021)
  460. A hybrid optimization approach to index tracking (2009)
  461. Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics (2018)
  462. Quantile regression for index tracking and enhanced indexation (2013)
  463. Minimal cost index tracking under nonlinear transactions costs and minimal transactions unit constraints (2001)
  464. Nonnegative-lasso and application in index tracking (2014)
  465. Nonnegative adaptive lasso for ultra-high dimensional regression models and a two-stage method applied in financial modeling (2016)
  466. Cointegration Portfolios of European Equities for Index Tracking and Market Neutral Strategies (2005)
  467. Indexing and Statistical Arbitrage: tracking error or cointegration? (2005)
  468. Minimizing the tracking error of cardinality constrained portfolios (2018)
  469. Factor-based robust index tracking (2017)
  470. Efficient Capital Markets: a review of theory and empirical work (1970)
  471. The Cross-Section of Expected Stock Returns (1992)
  472. Luck versus Skill in the Cross-Section of Mutual Fund Returns (2010)
  473. Mixed-integer programming approaches for index tracking and enhanced indexation (2009)
  474. Exact and Heuristic Approaches for the Index Tracking Problem with UCITS Constraints (2013)
  475. Kernel Search: an application to the index tracking problem (2012)
  476. ETF liquidation determinants (2018)
  477. Impact of leveraged ETF trading on the market quality of component stocks (2014)
  478. Exchange-traded funds: a market snapshot and performance analysis (2014)
  479. Minimizing Tracking Error While Restricting the Number of Assets (2006)
  480. Optimal Portfolio Selection and Dynamic Benchmark Tracking (2005)
  481. Index tracking with controlled number of assets using a hybrid heuristic combining genetic algorithm and non-linear programming (2017)
  482. Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis (2002)
  483. A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model (2004)
  484. A portfolio optimization model with three objectives and discrete variables (2010)
  485. Different approaches to risk estimation in portfolio theory (2004)
  486. Risk management with expectiles (2015)
  487. Conditional Value-at-Risk, spectral risk measures and (non-) diversification in portfolio selection problems–A comparison with mean–variance analysis (2013)
  488. Entropic risk measures and their comparative statics in portfolio selection: Coherence vs. convexity (2017)
  489. Two-sided coherent risk measures and their application in realistic portfolio optimization (2008)
  490. Comparing downside risk measures for heavy tailed distributions (2006)
  491. Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? (2009)
  492. Distorted probabilities and insurance premiums (1990)
  493. Putting order in risk measures (2002)
  494. Law invariant convex risk measures (2005)
  495. Tail Variance Premium with Applications for Elliptical Portfolio of Risks (2006)
  496. Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks (2017)
  497. Risk measures for asset allocation models (2004)
  498. Measuring Systemic Risk: A Comparison of Alternative Market-Based Approaches (2017)
  499. Higher moment coherent risk measures (2007)
  500. The proper use of risk measures in portfolio theory (2005)
  501. The 1/N investment strategy is optimal under high model ambiguity (2012)
  502. A quantitative comparison of risk measures (2017)
  503. Portfolio optimization and performance analysis (2007)
  504. Desirable properties of an ideal risk measure in portfolio theory (2008)
  505. Distortion risk measures in portfolio optimization (2010)
  506. Multi-attribute decision making: A simulation comparison of select methods (1998)
  507. Multiple criteria decision aiding for finance: An updated bibliographic survey (2015)
  508. Optimization of conditional value-at-risk (2000)
  509. Conditional value-at-risk for general loss distributions (2002)
  510. CVaR-LASSO Enhanced Index Replication ( CLEIR ): outperforming by minimizing downside risk (2019)
  511. Enhanced index tracking with CVaR -based ratio measures (2020)
  512. Enhanced indexing using weighted conditional value at risk (2019)
  513. Index tracking using a hybrid genetic algorithm (2005)
  514. Index tracking model, downside risk and non-parametric kernel estimation (2018)
  515. Portfolio frontiers with restrictions to tracking error volatility and value at risk (2012)
  516. Enhanced indexation based on second-order stochastic dominance (2013)
  517. Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios (2013)
  518. CVaR -cardinality enhanced indexation optimization with tunable short-selling constraints (2020)
  519. Cardinality versus q-norm constraints for index tracking (2014)
  520. Dynamic index tracking via stochastic programming (2019)
  521. An Evolutionary Heuristic for the Index Tracking Problem (2003)
  522. A mean-variance analysis of tracking error (1992)
  523. A mixed 0–1 LP for index tracking problem with CVaR risk constraints (2012)
  524. Package riskR (2015)
  525. Package ‘quantmod’ (2020)
  526. Index tracking and enhanced indexing using mixed conditional value-at-risk (2018)
  527. Financial contagion across major stock markets: A study during crisis episodes (2019)
  528. European bond ETFs: tracking errors and the sovereign debt crisis (2014)
  529. Dual Representation of Expectile based Expected Shortfall and Its Properties (2019) — link
  530. On a robust risk measurement approach for capital determination errors minimization (2020)
  531. Trade and currency options hedging model (2018)
  532. Energy commodities: A review of optimal hedging strategies (2019)
  533. Hedge effectiveness: Basis risk and minimum-variance hedging (2000)
  534. The optimal hedge strategy of crude oil spot and futures markets: Evidence from a novel method (2019)
  535. Optimal hedge ratio estimation and hedge effectiveness with multivariate skew distributions (2014)
  536. Hedge effectiveness: Basis risk and minimum-variance hedging (1992)
  537. Hedging with zero-value at risk hedge ratio (2006)
  538. Dynamic hedging performance and downside risk: Evidence from Nikkei index futures (2018)
  539. Optimal futures hedging for energy commodities: An application of the GAS model (2020)
  540. Hedging systematic risk in the commodity market with a regime-switching multivariate rotated generalized autoregressive conditional heteroskedasticity model (2018)
  541. A Copula-Based Quantile Risk Measure Approach to Estimate the Optimal Hedge Ratio (2014)
  542. Option hedging using LSTM-RNN : an empirical analysis (2021)
  543. The effects of skewness on hedging decisions: an application of the skew-normal distribution in WTI and Brent futures (2021)
  544. The effects of skewness on optimal production and hedging decisions: An application of the skew-normal distribution (2010)
  545. Hedging downside risk of oil refineries: A vine copula approach (2017)
  546. Sample average approximation of CVaR-based hedging problem with a deep-learning solution (2021)
  547. Dynamic hedging of conditional value-at-risk (2012)
  548. Set optimization of set-valued risk measures (2021)
  549. An efficient method for mitigating longevity value-at-risk (2021)
  550. Equal risk pricing and hedging of financial derivatives with convex risk measures (2021)
  551. Hedging an option portfolio with minimum transaction lots: A fuzzy goal programming problem (2016)
  552. On the optimal hedge ratio in index-based longevity risk hedging (2019)
  553. Measuring quantile risk hedging effectiveness: a GO-GARCH-EVT-copula approach (2020)
  554. An optimal multi-step quadratic risk-adjusted hedging strategy (2013)
  555. Estimation and hedging effectiveness of time-varying hedge ratio: Nonparametric approaches (2016)
  556. A generalized approach to optimal hedging with option contracts (2015)
  557. Optimal hedge ratio under a subjective re-weighting of the original measure (2016)
  558. Hedging emerging market stock prices with oil, gold, VIX , and bonds: A comparison between DCC, ADCC and GO-GARCH (2016)
  559. Analyzing hedging strategies for fixed income portfolios: A bayesian approach for model selection (2016)
  560. Insurance valuation: A two-step generalised regression approach (2022)
  561. A stochastic programming model for dynamic portfolio management with financial derivatives (2022)
  562. Replicating portfolio approach to capital calculation (2018)
  563. Static hedging of multivariate derivatives by simulation (2005)
  564. Pricing and hedging guaranteed annuity options via static option replication (2003)
  565. Dynamic option hedging with transaction costs: A stochastic model predictive control approach (2019)
  566. Arbitrage theory in continuous time (2009)
  567. Pricing and hedging in incomplete markets (2001)
  568. Pricing and hedging in incomplete markets with model uncertainty (2020)
  569. A robust approach for minimization of risk measurement errors (2017)
  570. Comparative and qualitative robustness for law-invariant risk measures (2014)
  571. Quantifying market risk with Value-at-Risk or Expected Shortfall? – Consequences for capital requirements and model risk (2016)
  572. THE CANONICAL MODEL SPACE FOR LAW-INVARIANT CONVEX RISK MEASURES IS L1 (2012)
  573. A theory for combinations of risk measures (2018) — link
  574. Entropy Coherent and Entropy Convex Measures of Risk (2013)
  575. Are law-invariant risk functions concave on distributions? (2013)
  576. Disentangling price, risk and model risk: V & R measures (2018)
  577. Risk measuring under model uncertainty (2012)
  578. Upper bounds for strictly concave distortion risk measures on moment spaces (2018)
  579. Measuring Model Risk in Financial Risk Management and Pricing (2020)
  580. Convex risk measures: Basic facts, law-invariance and beyond, asymptotics for large portfolios (2013)
  581. The Wasserstein Metric and Robustness in Risk Management (2016)
  582. Risk measures with the CxLS property (2016)
  583. Stochastic orders and risk measures: Consistency and bounds (2006)
  584. Characterization, Robustness and Aggregation of Signed Choquet Integrals (2017)
  585. Distributionally robust shortfall risk optimization model and its approximation (2019)
  586. Fatou closedness under model uncertainty (2018)
  587. On the dual representation of coherent risk measures (2018)
  588. Closed-Form Solutions for Extreme-Case Distortion Risk Measures and Applications to Robust Portfolio Management (2018)
  589. Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization (2017)
  590. Law invariant convex risk measures for portfolio vectors (2006)
  591. On comonotonicity of Pareto optimal risk sharing (2008)
  592. Model risk measures: A review and new proposals on risk forecasting (2020)
  593. Optimal Risk Sharing for Law Invariant Monetary Utility Functions (2008)
  594. External Risk Measures and Basel Accords (2013)
  595. Cash Subadditive Risk Measures and Iterest Rate Ambiguity (2009)
  596. Risk Measures: Rationality and Diversification (2011)
  597. Mathematical Risk Analysis (2013)
  598. Acceptability maximization (2020) — link
  599. Acceptability Indexes for Portfolio Vectors (2019)
  600. Acceptability Indexes Via ‘g-Expectations’: An Application to Liquidity Risk (2013)
  601. A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time (2017)
  602. Dynamic Coherent Acceptability Indices and their Applications to Finance (2014)
  603. Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices (2013)
  604. Dynamic Assessment Indices (2016)
  605. New Measures for Performance Evaluation (2009)
  606. The Best Gain-Loss Ratio is a Poor Performance Measure (2013)
  607. Dynamic quasi-concave performance measures (2014)
  608. Acceptability indices of performance for bounded càdlàg processes (2020)
  609. Upside beta ratio: A performance measure for potential-seeking investors (2020)
  610. Portfolio performance evaluation with loss aversion (2014)
  611. Ranking of Investment Funds: Acceptability Vs Robustness (2015)
  612. Risk Preferences and Their Robust Representation (2013)
  613. When all risk-adjusted performance measures are the same: in praise of the Sharpe ratio (2011)
  614. Generalized Performance Ratios and Risk Optimization (2016)
  615. Weakening the Gain-Loss-Ratio measure to make it stronger (2015)
  616. When all risk-adjusted performance measures are the same: in praise of the Sharpe ratio ‐ a comment (2014)
  617. On the Consistent Use of VaR in Portfolio Performance Evaluation: A Cautionary Note (2010)
  618. Star-shaped Risk Measures (2021) — link
  619. Monotone Sharpe ratios and related measures of investment performance (2021)
  620. Risk sharing under heterogeneous beliefs without convexity (2021) — link
  621. Liquidity risk theory and coherent measures of risk (2008)
  622. Liquidity, Risk Measures, and Concentration of Measure (2018)
  623. On the link between monetary and star-shaped risk measures (2022)
  624. Can a Coherent Risk Measure Be Too Subadditive? (2008)
  625. Risk Aversion in Regulatory Capital Principles (2020)
  626. Risk measures based on benchmark loss distributions (2020)
  627. Sensitivity to large losses and $\rho$-arbitrage for convex risk measures (2022) — link
  628. Star-shaped acceptability indexes (2021) — link
  629. Monetary Risk Measures (2020) — link
  630. A decomposition of general premium principles into risk and deviation (2021)
  631. Law invariant convex risk measures (2005)
  632. A Theory for Measures of Tail Risk (2021)
  633. Quantifying market risk with Value-at-Risk or Expected Shortfall? – Consequences for capital requirements and model risk (2016)
  634. Is the Inf-convolution of Law-invariant Preferences Law-invariant? (2020)
  635. Quantile-Based Risk Sharing (2018)
  636. Solvency II, or how to sweep the downside risk under the carpet (2018)
  637. Inf-Convolution of Choquet Integrals and Applications in Optimal Risk Transfer (2017)
  638. Modelling agents’ preferences in complete markets by second order stochastic dominance (2003)
  639. Non-additivie Measure and Intgral (1994)
  640. Co-monotone allocations, Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion (1994)
  641. Hedging bounded claims with bounded outcomes (2006)
  642. Characterizing optimal allocations in quantile-based risk sharing (2018)
  643. Risk sharing for capital requirements with multidimensional security markets (2019)
  644. Optimal risk sharing with non-monotone monetary functionals (2007)
  645. Optimal risk sharing with different reference probabilities (2009)
  646. Allocation of risks and equilibrium in markets with finitely many traders (2008)
  647. On comonotonicity of Pareto optimal risk sharing (2008)
  648. Quantile-based risk sharing with heterogeneous beliefs (2020)
  649. Pareto Equilibria with coherent measures of risk (2004)
  650. Optimal capital and risk allocations for law- and cash-invariant convex functions (2008)
  651. Short note on inf-convolution preserving the Fatou property (2009)
  652. Pareto optimal allocations and optimal risk sharing for quasiconvex risk measures (2015)
  653. Pareto efficiency for the concave order and multivariate comonotonicity (2012)
  654. OVERLAPPING SETS OF PRIORS AND THE EXISTENCE OF EFFICIENT ALLOCATIONS AND EQUILIBRIA FOR RISK MEASURES (2010)
  655. To split or not to split: Capital allocation with convex risk measures (2009)
  656. Model risk measures: A review and new proposals on risk forecasting (2020)
  657. Inf-convolution and Optimal Allocations for Tail Risk Measures (2019)
  658. Optimal risk sharing under distorted probabilities (2009)
  659. Optimal risk sharing with general deviation measures (2012)
  660. On the optimal risk allocation problem (2006)
  661. Pareto-Optimal Risk Exchanges and Related Decision Problems (1978)
  662. The general economic premium principle (1982)
  663. Equilibrium in a reinsurance market (1962)
  664. Uncertainty and Welfare Economics of Medica Care (1963)
  665. A Fubini-type theorem for finitely additive measure spaces (1974)
  666. Superquantile/CVaR risk measures: second-order theory (2018)
  667. Dual Representation of Expectile based Expected Shortfall and Its Properties (2021)
  668. Superquantiles and their applications to risk, random variables, and regression (2013)
  669. Random variables, monotone relations, and convex analysis (2014)
  670. Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk (2014)
  671. Quantitative Statistical Robustness for Tail-Dependent Law Invariant Risk Measures (2021)
  672. Elicitability of Range Value at Risk (2019)
  673. A Monte Carlo evaluation of non-parametric estimators of expected shortfall (2020)
  674. Estimation of extreme value-at-risk: An EVT approach for quantile GARCH model (2014)
  675. Robust backtesting tests for value-at-risk models (2011)
  676. Estimation risk in financial risk management (2005)
  677. Volatility specifications versus probability distributions in VaR forecasting (2021)
  678. A New Approach to the Quantification of Model Risk for Practitioners (2019)
  679. Efficient tests for normality, homoscedasticity and serial independence of regression residuals (1980)
  680. A new look at the statistical model identification (1974)
  681. Forecasting Bitcoin risk measures: A robust approach (2019)
  682. GARCH models: structure, statistical inference and financial applications (2019)
  683. Empirical analysis of GARCH models in value at risk estimation (2006)
  684. GARCH models for daily stock returns: impact of estimation frequency on Value-at-Risk and Expected Shortfall forecasts (2014)
  685. On conditional risk estimation considering model risk (2016)
  686. A cost-benefit analysis of capital requirements adjusted for model risk (2020)
  687. A varying-coefficient expectile model for estimating value at risk (2014)
  688. Measuring the risk of Chinese Fintech industry: evidence from the stock index (2021)
  689. On the existence of an optimal estimation window for risk measures (2016)
  690. Estimating value-at-risk and expected shortfall using the intraday low and range data (2020)
  691. Cryptocurrencies value-at-risk and expected shortfall: Do regime-switching volatility models improve forecasting? (2020)
  692. Fundamental review of the trading book: a revised market risk framework. (2013)
  693. Range Value-at-Risk : multivariate and extreme values (2020)
  694. Range Value-at-Risk bounds for unimodal distributions under partial information (2020)
  695. Some remarks on the value-at-risk and the conditional value-at-risk (2000)
  696. Relative bound and asymptotic comparison of expectile with respect to expected shortfall (2020)
  697. Tail expectile process and risk assessment (2020)
  698. Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings (2016)
  699. Filtered extreme-value theory for value-at-risk estimation: evidence from Turkey (2010)
  700. Deviation-based model risk measures (2021)
  701. The expected-based value-at-risk and expected shortfall using quantile and expectile with application to electricity market data (2021)
  702. A comparison of GARCH models for VaR estimation (2012)
  703. Evaluating Range Value at Risk forecasts (2020)
  704. Multinomial Backtesting of Distortion Risk Measures (2022)
  705. PELVE: Probability Equivalent Level of VaR and ES (2020)
  706. Quantifying market risk with Value-at-Risk or Expected Shortfall? Consequences for capital requirements and model risk (2016)
  707. Backtesting expected shortfall (2014)
  708. On the elicitability of range value at risk (2021)
  709. A general and adaptive robust loss function (2019)
  710. Robust estimation of a location parameter (1992)
  711. Techniques for nonlinear least squares and robust regression (1978)
  712. A Bayesian approach to real estate assessment (1975)
  713. The location of a minimum variance squared distance functional (2022)
  714. Bayesian estimation and prediction using asymmetric loss functions (1986)
  715. Mathematical Risk Analysis (2013)
  716. Convex risk measures: Basic facts, law-invariance and beyond, asymptotics for large portfolios (2013)
  717. Subdifferential representations of risk measures (2006)
  718. An optimal multi-step quadratic risk-adjusted hedging strategy (2013)
  719. Pricing and hedging in incomplete markets (2001)
  720. Pricing and hedging in incomplete markets with model uncertainty (2020)
  721. Analyzing hedging strategies for fixed income portfolios: A bayesian approach for model selection (2016)
  722. Energy commodities: A review of optimal hedging strategies (2019)
  723. Insurance valuation: A two-step generalised regression approach (2022)
  724. Star-shaped acceptability indexes (2021) — link
  725. On the link between monetary and star-shaped risk measures (2022)
  726. Sensitivity to large losses and $\rho$-arbitrage for convex risk measures (2022) — link
  727. From stochastic dominance to mean-risk models: Semideviations as risk measures (1999)
  728. Bayesian estimation and prediction using asymmetric loss functions (1986)
  729. Techniques for nonlinear least squares and robust regression (1978)
  730. A varying-coefficient expectile model for estimating valueat risk (2014)
  731. Measuring the risk of Chinese Fintech industry: evidence fromthe stock index (2021)
  732. Hedging with linear regressions and neural networks (2021)
  733. Dynamic Risk Measures (2011) — link
  734. Topologies on closed and closed convex sets (1993)
  735. On the Extension of the Namioka-Klee Theorem and on the Fatou Property for Risk Measures (2010) — link
  736. Integration with Respect to Finitely Additive Measures (1991)
  737. On regular extensions of measures (1980)
  738. Theory of extremal problems (1979)
  739. Spectral measures of risk: A coherent representation of subjective risk aversion (2002)
  740. Subdifferential representations of risk measures (2006)
  741. Diversification, protection of liability holders and regulatory arbitrage (2017)
  742. Computational aspects of robust optimized certainty equivalents and option pricing (2019)
  743. A theory for combinations of risk measures (2023)
  744. Risk measuring under model uncertainty (2012)
  745. Risk capital allocation by coherent risk measures based on one-sided moments (2003)
  746. From stochastic dominance to mean-risk models: Semideviations as risk measures (1999)
  747. Law-invariant risk measures: Extension properties and qualitative robustness (2014)
  748. Stochastic orders and risk measures: Consistency and bounds (2006)
  749. Portfolio Selection (1952)
  750. Distributionally robust shortfall risk optimization model and its approximation (2019)
  751. Law invariant convex risk measures for portfolio vectors (2006)
  752. On comonotonicity of Pareto optimal risk sharing (2008)
  753. Model risk measures: A review and new proposals on risk forecasting (2020)
  754. Risk Measures: Rationality and Diversification (2011)
  755. Mathematical Risk Analysis (2013)
  756. A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time (2017)
  757. Performance measurement with expectiles (2022)
  758. Lotteries, insurance, and star-shaped utility functions (1990) — link
  759. Applied Conic Finance (2016)
  760. Gain, loss, and asset pricing (2000)
  761. Lopsided convergence: an extension and its quantification (2019)
  762. Set-convergence and its application: A tutorial (2020)
  763. Risk measures for non-integrable random variables (2009)
  764. On the C-property and-representations of risk measures (2018)
  765. Law invariant risk measures on $L^\infty (\mathbb R ^d) $L (2011)
  766. Comonotonic measures of multivariate risks (2012)
  767. Coherent and convex risk measures for portfolios with applications (2014)
  768. Scalar multivariate risk measures with a single eligible asset (2022)
  769. An axiomatic approach to systemic risk (2013)
  770. Systemic risk measures on general measurable spaces (2016)
  771. On fairness of systemic risk measures (2020)
  772. Coherent and convex monetary risk measures for bounded cadlag processes (2004)
  773. Coherent and convex monetary risk measures for unbounded cadlag processes (2005)
  774. Risk measures and capital requirements for processes (2006)
  775. Convex risk measures for Cadlag processes on Orlicz hearts (2014)
  776. Risk measures on the space of infinite sequences (2010)
  777. Vector-valued coherent risk measures (2004)
  778. Duality for set-valued measures of risk (2010)
  779. Set-valued shortfall and divergence risk measures (2017)
  780. Set-valued risk measures for conical market models (2011)
  781. A framework for measures of risk under uncertainty (2024)
  782. Monetary Utility Functions on $ C_b (X) $ Spaces (2022) — link
  783. Worst-case conditional V alue-at- R isk with application to robust portfolio management (2009)
  784. Analytical bounds for two V alue-at- R isk functionals (2002)
  785. Constructing risk measures from uncertainty sets (2009)
  786. Robust risk-aware reinforcement learning (2022)
  787. Distributionally robust optimization with decision dependent ambiguity sets (2020)
  788. Robust solutions of optimization problems affected by uncertain probabilities (2013)
  789. Ambiguous risk measures and optimal robust portfolios (2007)
  790. Likelihood robust optimization for data-driven problems (2016)
  791. Robust distortion risk measures (2023)
  792. Uncertainty Propagation and Dynamic Robust Risk Measures — → 2308.12856
  793. On the role of norm constraints in portfolio selection (2011)
  794. Robust portfolio techniques for mitigating the fragility of CVaR minimization and generalization to coherent risk measures (2013)
  795. Ambiguity in portfolio selection (2007)
  796. Data-driven distributionally robust optimization using the W asserstein metric: Performance guarantees and tractable reformulations (2018)
  797. Distributionally robust stochastic optimization with W asserstein distance (2022)
  798. Portfolio optimisation within a W asserstein ball (2020)
  799. Set-valued convex analysis (2009)
  800. Variational principles on metric and uniform spaces (2005)
  801. Systemic risk measures on general measurable spaces (2016)
  802. Capital allocation rules and acceptance sets (2020)
  803. Different kinds of risk (2009)
  804. Coherent diversification measures in portfolio theory: An axiomatic foundation (2022)
  805. Diversification quotients: Quantifying diversification via risk measures (2022) — link
  806. Inf-convolution and optimal risk sharing with countable sets of risk measures (2022)
  807. Dynamic monetary risk measures for bounded discrete-time processes (2006)
  808. Dynamic coherent risk measures (2004)
  809. Coherent multiperiod risk adjusted values and B ellman’s principle (2007)
  810. Lectures on stochastic programming: modeling and theory (2021)
  811. Lower semicontinuity of monotone functionals in the mixed topology on $ C_b$ (2024) — link

10 of 819 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.