Impact IRR: Leveraging Modern Portfolio Theory to Define Impact Investments ArXiv ID: 2509.22600 “View on arXiv” Authors: Daniel Soliman Abstract The impact investment market has an estimated value of almost $1.6 trillion. Significant progress has been made in determining the financial returns of impact investing. Investors are still, however, in the early stages of determining impact return. In this study, the author proposes the use of impact internal rate of return (impact IRR) to evaluate and monitor impact investments. This approach, which utilizes components of modern portfolio theory, adapted financial tools, and existing datasets, is demonstrated herein through initial use cases and examples showing how it can be employed to optimize impact. ...

Optimal Consumption-Investment with Epstein-Zin Utility under Leverage Constraint ArXiv ID: 2509.21929 “View on arXiv” Authors: Dejian Tian, Weidong Tian, Jianjun Zhou, Zimu Zhu Abstract We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, by developing a new dynamic programming principle under constraints. We further demonstrate that the value function admits smoothness and characterize the optimal consumption and investment strategies. In addition, we derive explicit solutions for the optimal strategy and explicitly delineate the constrained and unconstrained regions in several special cases of the leverage constraint. Finally, we conduct a comparative analysis, highlighting the differences relative to the classical time-separable preferences and to the setting without leverage constraints. ...

Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspective ArXiv ID: 2509.22896 “View on arXiv” Authors: Peng Xu Abstract This paper develops stochastic optimization problems for describing and analyzing behavioral investors with Markowitz Stochastic Dominance (MSD) preferences. Specifically, we establish dominance conditions in a discrete state-space to capture all reverse S-shaped MSD preferences as well as all subjective decision weights generated by inverse S-shaped probability weighting functions. We demonstrate that these dominance conditions can be admitted as linear constraints into the stochastic optimization problems to formulate computationally tractable mixed-integer linear programming (MILP) models. We then employ the developed MILP models in financial portfolio analysis and examine classic behavioral factors such as reference point and subjective probability distortion in behavioral investors’ portfolio decisions. ...

Selection Confidence Sets for Equally Weighted Portfolios ArXiv ID: 2510.14988 “View on arXiv” Authors: Davide Ferrari, Alessandro Fulci, Sandra Paterlini Abstract Given a universe of N assets, investors often form equally weighted portfolios (EWPs) by selecting subsets of assets. EWPs are simple, robust, and competitive out-of-sample, yet the uncertainty about which subset truly performs best is largely ignored. Traditional approaches typically rely on a single selected portfolio, but this fails to consider alternative investment strategies that may perform just as well when accounting for statistical uncertainty. To address this selection uncertainty, we introduce the Selection Confidence Set (SCS) for EWPs: the set of all portfolios that, under a given loss function and at a specified confidence level, contains the unknown set of optimal portfolios under repeated sampling. The SCS quantifies selection uncertainty by identifying a range of plausible portfolios, challenging the idea of a uniquely optimal choice. Like a confidence set, its size reflects uncertainty – growing with noisy or limited data, and shrinking as the sample size increases. Theoretically, we establish that the SCS covers the unknown optimal selection with high probability and characterize how its size grows with underlying uncertainty, corroborating these results through Monte Carlo experiments. Applications to the French 17-Industry Portfolios and Layer-1 cryptocurrencies underscore the importance of accounting for selection uncertainty when comparing equally weighted strategies. ...

Multivariate Quadratic Hawkes Processes – Part II: Non-Parametric Empirical Calibration ArXiv ID: 2509.21244 “View on arXiv” Authors: Cecilia Aubrun, Michael Benzaquen, Jean-Philippe Bouchaud Abstract This is the second part of our work on Multivariate Quadratic Hawkes (MQHawkes) Processes, devoted to the calibration of the model defined and studied analytically in Aubrun, C., Benzaquen, M., & Bouchaud, J. P., Quantitative Finance, 23(5), 741-758 (2023). We propose a non-parametric calibration method based on the general method of moments applied to a coarse-grained version of the MQHawkes model. This allows us to bypass challenges inherent to tick by tick data. Our main methodological innovation is a multi-step calibration procedure, first focusing on ‘‘self’’ feedback kernels, and then progressively including cross-effects. Indeed, while cross-effects are significant and interpretable, they are usually one order of magnitude smaller than self-effects, and must therefore be disentangled from noise with care. For numerical stability, we also restrict to pair interactions and only calibrate bi-variate QHawkes, neglecting higher-order interactions. Our main findings are: (a) While cross-Hawkes feedback effects have been empirically studied previously, cross-Zumbach effects are clearly identified here for the first time. The effect of recent trends of the E-Mini futures contract onto the volatility of other futures contracts is especially strong; (b) We have identified a new type of feedback that couples past realized covariance between two assets and future volatility of these two assets, with the pair E-Mini vs TBOND as a case in point; (c) A cross-leverage effect, whereby the sign of the return of one asset impacts the volatility of another asset, is also clearly identified. The cross-leverage effect between the E-Mini and the residual volatility of single stocks is notable, and surprisingly universal across the universe of stocks that we considered. ...

Error Propagation in Dynamic Programming: From Stochastic Control to Option Pricing ArXiv ID: 2509.20239 “View on arXiv” Authors: Andrea Della Vecchia, Damir Filipović Abstract This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options. ...

Long-Range Dependence in Financial Markets: Empirical Evidence and Generative Modeling Challenges ArXiv ID: 2509.19663 “View on arXiv” Authors: Yifan He, Svetlozar Rachev Abstract This study presents a comprehensive empirical investigation of the presence of long-range dependence (LRD) in the dynamics of major U.S. stock market indexes–S&P 500, Dow Jones, and Nasdaq–at daily, weekly, and monthly frequencies. We employ three distinct methods: the classical rescaled range (R/S) analysis, the more robust detrended fluctuation analysis (DFA), and a sophisticated ARFIMA–FIGARCH model with Student’s $t$-distributed innovations. Our results confirm the presence of LRD, primarily driven by long memory in volatility rather than in the mean returns. Building on these findings, we explore the capability of a modern deep learning approach, Quant generative adversarial networks (GANs), to learn and replicate the LRD observed in the empirical data. While Quant GANs effectively capture heavy-tailed distributions and some aspects of volatility clustering, they suffer from significant limitations in reproducing the LRD, particularly at higher frequencies. This work highlights the challenges and opportunities in using data-driven models for generating realistic financial time series that preserve complex temporal dependencies. ...

Roughness Analysis of Realized Volatility and VIX through Randomized Kolmogorov-Smirnov Distribution ArXiv ID: 2509.20015 “View on arXiv” Authors: Sergio Bianchi, Daniele Angelini Abstract We introduce a novel distribution-based estimator for the Hurst parameter of log-volatility, leveraging the Kolmogorov-Smirnov statistic to assess the scaling behavior of entire distributions rather than individual moments. To address the temporal dependence of financial volatility, we propose a random permutation procedure that effectively removes serial correlation while preserving marginal distributions, enabling the rigorous application of the KS framework to dependent data. We establish the asymptotic variance of the estimator, useful for inference and confidence interval construction. From a computational standpoint, we show that derivative-free optimization methods, particularly Brent’s method and the Nelder-Mead simplex, achieve substantial efficiency gains relative to grid search while maintaining estimation accuracy. Empirical analysis of the CBOE VIX index and the 5-minute realized volatility of the S&P 500 reveals a statistically significant hierarchy of roughness, with implied volatility smoother than realized volatility. Both measures, however, exhibit Hurst exponents well below one-half, reinforcing the rough volatility paradigm and highlighting the open challenge of disentangling local roughness from long-memory effects in fractional modeling. ...

Connecting Quantum Computing with Classical Stochastic Simulation ArXiv ID: 2509.18614 “View on arXiv” Authors: Jose Blanchet, Mark S. Squillante, Mario Szegedy, Guanyang Wang Abstract This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover’s algorithm for unstructured search to build intuition. We then move slowly to amplitude estimation problems and applications to counting and Monte Carlo integration, again using Grover-type iterations. A hands-on Python/Qiskit implementation illustrates these concepts applied to finance. The paper concludes with a discussion on current challenges in scaling quantum simulation techniques. ...

Filtering amplitude dependence of correlation dynamics in complex systems: application to the cryptocurrency market ArXiv ID: 2509.18820 “View on arXiv” Authors: Marcin Wątorek, Marija Bezbradica, Martin Crane, Jarosław Kwapień, Stanisław Drożdż Abstract Based on the cryptocurrency market dynamics, this study presents a general methodology for analyzing evolving correlation structures in complex systems using the $q$-dependent detrended cross-correlation coefficient ρ(q,s). By extending traditional metrics, this approach captures correlations at varying fluctuation amplitudes and time scales. The method employs $q$-dependent minimum spanning trees ($q$MSTs) to visualize evolving network structures. Using minute-by-minute exchange rate data for 140 cryptocurrencies on Binance (Jan 2021-Oct 2024), a rolling window analysis reveals significant shifts in $q$MSTs, notably around April 2022 during the Terra/Luna crash. Initially centralized around Bitcoin (BTC), the network later decentralized, with Ethereum (ETH) and others gaining prominence. Spectral analysis confirms BTC’s declining dominance and increased diversification among assets. A key finding is that medium-scale fluctuations exhibit stronger correlations than large-scale ones, with $q$MSTs based on the latter being more decentralized. Properly exploiting such facts may offer the possibility of a more flexible optimal portfolio construction. Distance metrics highlight that major disruptions amplify correlation differences, leading to fully decentralized structures during crashes. These results demonstrate $q$MSTs’ effectiveness in uncovering fluctuation-dependent correlations, with potential applications beyond finance, including biology, social and other complex systems. ...