Robust risk evaluation of joint life insurance under dependence uncertainty

2025-10-02

AI Summary

Modeling multivariate mortality dependence in joint-life insurance is challenged by data scarcity, leading to significant uncertainty in dependence structure specification and consequent pricing and risk assessment inaccuracies. Method: This paper proposes a robust pricing and risk evaluation framework grounded in reference vine copula structures. Leveraging the monotonicity of distortion risk measures with respect to concordance order, we derive the most conservative and most aggressive risk bounds. Under a norm-ball–defined ambiguity set for dependence, we efficiently compute tight upper and lower bounds for the mean, Value-at-Risk (VaR), and expected shortfall via linear programming. Contribution/Results: To our knowledge, this is the first work embedding vine copulas into robust dependence modeling, substantially improving the sharpness of existing risk bounds. Numerical experiments reveal heterogeneous sensitivity of optimal vine selection to both risk measure type and policy structure. Empirical results demonstrate that the proposed method markedly enhances the robustness and discriminative power of risk assessment under limited data.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Natural Language Processing: Safety and Robustness
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Dependence among multiple lifetimes is a key factor for pricing and evaluating the risk of joint life insurance products. The dependence structure can be exposed to model uncertainty when available data and information are limited. We address robust pricing and risk evaluation of joint life insurance products against dependence uncertainty among lifetimes. We first show that, for some class of standard contracts, the risk evaluation based on distortion risk measure is monotone with respect to the concordance order of the underlying copula. Based on this monotonicity, we then study the most conservative and anti-conservative risk evaluations for this class of contracts. We prove that the bounds for the mean, Value-at-Risk and Expected shortfall are computed by a combination of linear programs when the uncertainty set is defined by some norm-ball centered around a reference copula. Our numerical analysis reveals that the sensitivity of the risk evaluation against the choice of the copula differs depending on the risk measure and the type of the contract, and our proposed bounds can improve the existing bounds based on the available information.

Problem

• Joint life insurance risk evaluation under dependence uncertainty
• Robust pricing against copula model uncertainty
• Conservative bounds for risk measures via linear programming

Innovation

• Uses distortion risk measures for monotonicity analysis
• Computes bounds via linear programming for copula uncertainty
• Improves existing bounds using reference copula information