Insurance

Optimized Multi-Level Monte Carlo Parametrization and Antithetic Sampling for Nested Simulations ArXiv ID: 2510.18995 “View on arXiv” Authors: Alexandre Boumezoued, Adel Cherchali, Vincent Lemaire, Gilles Pagès, Mathieu Truc Abstract Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC) techniques and their weighted variants are typically more efficient, their effectiveness tends to deteriorate when dealing with irregular functions, notably indicator functions, which are intrinsic to these risk measures. We address this issue by introducing a novel MLMC parametrization that significantly improves performance in practical, non-asymptotic settings while maintaining theoretical asymptotic guarantees. We also prove that antithetic sampling of MLMC levels enhances efficiency regardless of the regularity of the underlying function. Numerical experiments motivated by the calculation of economic capital in a life insurance context confirm the practical value of our approach for estimating loss probabilities and quantiles, bridging theoretical advances and practical requirements in financial risk estimation. ...

Model Monitoring: A General Framework with an Application to Non-life Insurance Pricing ArXiv ID: 2510.04556 “View on arXiv” Authors: Alexej Brauer, Paul Menzel, Mario V. Wüthrich Abstract Maintaining the predictive performance of pricing models is challenging when insurance portfolios and data-generating mechanisms evolve over time. Focusing on non-life insurance, we adopt the concept-drift terminology from machine learning and distinguish virtual drift from real concept drift in an actuarial setting. Methodologically, we (i) formalize deviance loss and Murphy’s score decomposition to assess global and local auto-calibration; (ii) study the Gini score as a rank-based performance measure, derive its asymptotic distribution, and develop a consistent bootstrap estimator of its asymptotic variance; and (iii) combine these results into a statistically grounded, model-agnostic monitoring framework that integrates a Gini-based ranking drift test with global and local auto-calibration tests. An application to a modified motor insurance portfolio with controlled concept-drift scenarios illustrates how the framework guides decisions on refitting or recalibrating pricing models. ...

Variable annuities: A closer look at ratchet guarantees, hybrid contract designs, and taxation ArXiv ID: 2507.07358 “View on arXiv” Authors: Jennifer Alonso-Garcia, Len Patrick Dominic M. Garces, Jonathan Ziveyi Abstract This paper investigates optimal withdrawal strategies and behavior of policyholders in a variable annuity (VA) contract with a guaranteed minimum withdrawal benefit (GMWB) rider incorporating taxation and a ratchet mechanism for enhancing the benefit base during the life of the contract. Mathematically, this is accomplished by solving a backward dynamic programming problem associated with optimizing the discounted risk-neutral expectation of cash flows from the contract. Furthermore, reflecting traded VA contracts in the market, we consider hybrid products providing policyholders access to a cash fund which functions as an intermediate repository of earnings from the VA and earns interest at a contractually specified cash rate. We contribute to the literature by revealing several significant interactions among taxation, the cash fund, and the benefit base update mechanism. When tax rates are high, the tax-shielding effect of the cash fund, which is taxed differently from ordinary withdrawals from the VA, plays a significant role in enhancing the attractiveness of the overall contract. Furthermore, the ratchet benefit base update scheme (in contrast to the ubiquitous return-of-premium specification in the literature) tends to discourage early surrender as it provides enhanced downside market risk protection. In addition, the cash fund discourages active withdrawals, with policyholders preferring to transfer the guaranteed withdrawal amount to the cash fund to leverage the cash fund rate. ...

Systemic Risk in the European Insurance Sector ArXiv ID: 2505.02635 “View on arXiv” Authors: Giovanni Bonaccolto, Nicola Borri, Andrea Consiglio, Giorgio Di Giorgio Abstract This paper investigates the dynamic interdependencies between the European insurance sector and key financial markets-equity, bond, and banking-by extending the Generalized Forecast Error Variance Decomposition framework to a broad set of performance and risk indicators. Our empirical analysis, based on a comprehensive dataset spanning January 2000 to October 2024, shows that the insurance market is not a passive receiver of external shocks but an active contributor in the propagation of systemic risk, particularly during periods of financial stress such as the subprime crisis, the European sovereign debt crisis, and the COVID-19 pandemic. Significant heterogeneity is observed across subsectors, with diversified multiline insurers and reinsurance playing key roles in shock transmission. Moreover, our granular company-level analysis reveals clusters of systemically central insurance companies, underscoring the presence of a core group that consistently exhibits high interconnectivity and influence in risk propagation. ...

Modern Computational Methods in Reinsurance Optimization: From Simulated Annealing to Quantum Branch & Bound ArXiv ID: 2504.16530 “View on arXiv” Authors: George Woodman, Ruben S. Andrist, Thomas Häner, Damian S. Steiger, Martin J. A. Schuetz, Helmut G. Katzgraber, Marcin Detyniecki Abstract We propose and implement modern computational methods to enhance catastrophe excess-of-loss reinsurance contracts in practice. The underlying optimization problem involves attachment points, limits, and reinstatement clauses, and the objective is to maximize the expected profit while considering risk measures and regulatory constraints. We study the problem formulation, paving the way for practitioners, for two very different approaches: A local search optimizer using simulated annealing, which handles realistic constraints, and a branch & bound approach exploring the potential of a future speedup via quantum branch & bound. On the one hand, local search effectively generates contract structures within several constraints, proving useful for complex treaties that have multiple local optima. On the other hand, although our branch & bound formulation only confirms that solving the full problem with a future quantum computer would require a stronger, less expensive bound and substantial hardware improvements, we believe that the designed application-specific bound is sufficiently strong to serve as a basis for further works. Concisely, we provide insurance practitioners with a robust numerical framework for contract optimization that handles realistic constraints today, as well as an outlook and initial steps towards an approach which could leverage quantum computers in the future. ...

Dynamic Asset Pricing Theory for Life Contingent Risks ArXiv ID: 2503.21256 “View on arXiv” Authors: Unknown Abstract Although the valuation of life contingent assets has been thoroughly investigated under the framework of mathematical statistics, little financial economics research pays attention to the pricing of these assets in a non-arbitrage, complete market. In this paper, we first revisit the Fundamental Theorem of Asset Pricing (FTAP) and the short proof of it. Then we point out that discounted asset price is a martingale only when dividends are zero under all random states of the world, using a simple proof based on pricing kernel. Next, we apply Fundamental Theorem of Asset Pricing (FTAP) to find valuation formula for life contingent assets including life insurance policies and life contingent annuities. Last but not least, we state the assumption of static portfolio in a dynamic economy, and clarify the FTAP that accommodates the valuation of a portfolio of life contingent policies. ...

Decoding Financial Health in Kenyas’ Medical Insurance Sector: A Data-Driven Cluster Analysis ArXiv ID: 2502.17072 “View on arXiv” Authors: Unknown Abstract This study examines insurance companies’ financial performance and reporting trends within the medical sector using advanced clustering techniques to identify distinct patterns. Four clusters were identified by analyzing financial ratios and time series data, each representing unique financial performance and reporting consistency combinations. Dynamic Time Warping (DTW) and KMeans clustering were employed to capture temporal variations and uncover key insights into company behaviors. The findings reveal that resilient performers consistently report and have financial stability, making them reliable options for policyholders. In contrast, clusters of underperforming companies and those with reporting gaps highlight operational challenges and issues related to data consistency. These insights emphasize the importance of transparency and timely reporting to ensure the sector’s resilience. This study contributes to the literature by integrating time series analysis into financial clustering, offering practical recommendations for improving data governance and financial stability in the insurance sector. Future research could further investigate non-financial indicators and explore alternative clustering methods to provide a deeper understanding of performance dynamics. ...

Dynamic Investment-Driven Insurance Pricing and Optimal Regulation ArXiv ID: 2410.18432 “View on arXiv” Authors: Unknown Abstract This paper analyzes the equilibrium of insurance market in a dynamic setting, focusing on the interaction between insurers’ underwriting and investment strategies. Three possible equilibrium outcomes are identified: a positive insurance market, a zero insurance market, and market failure. Our findings reveal why insurers may rationally accept underwriting losses by setting a negative safety loading while relying on investment profits, particularly when there is a negative correlation between insurance gains and financial returns. Additionally, we explore the impact of regulatory frictions, showing that while imposing a cost on investment can enhance social welfare under certain conditions, it may not always be necessary. ...

Loss Aversion and State-Dependent Linear Utility Functions for Monetary Returns ArXiv ID: 2410.19030 “View on arXiv” Authors: Unknown Abstract We present a theory of expected utility with state-dependent linear utility functions for monetary returns, that incorporates the possibility of loss-aversion. Our results relate to first order stochastic dominance, mean-preserving spread, increasing-concave linear utility profiles and risk aversion. As an application of the expected utility theory developed here, we analyze the contract that a monopolist would offer in an insurance market that allowed for partial coverage of loss. ...

Cyber Risk Taxonomies: Statistical Analysis of Cybersecurity Risk Classifications ArXiv ID: 2410.05297 “View on arXiv” Authors: Unknown Abstract Cyber risk classifications are widely used in the modeling of cyber event distributions, yet their effectiveness in out of sample forecasting performance remains underexplored. In this paper, we analyse the most commonly used classifications and argue in favour of switching the attention from goodness-of-fit and in-sample predictive performance, to focusing on the out-of sample forecasting performance. We use a rolling window analysis, to compare cyber risk distribution forecasts via threshold weighted scoring functions. Our results indicate that business motivated cyber risk classifications appear to be too restrictive and not flexible enough to capture the heterogeneity of cyber risk events. We investigate how dynamic and impact-based cyber risk classifiers seem to be better suited in forecasting future cyber risk losses than the other considered classifications. These findings suggest that cyber risk types provide limited forecasting ability concerning cyber event severity distribution, and cyber insurance ratemakers should utilize cyber risk types only when modeling the cyber event frequency distribution. Our study offers valuable insights for decision-makers and policymakers alike, contributing to the advancement of scientific knowledge in the field of cyber risk management. ...