Benchmark-Neutral Risk-Minimization for insurance products and nonreplicable claims

2025-06-24

AI Summary

This study addresses pricing and hedging challenges for non-replicable or contingent-claim-based long-term insurance products—such as variable annuities—in incomplete markets, aiming to eliminate insurance–financial arbitrage and enhance long-term risk management. Method: We adopt Platen’s (2024) benchmark-neutral pricing framework, using the growth-optimal portfolio as the numéraire to construct a benchmark-neutral measure—replacing the conventional risk-neutral measure—to mitigate overvaluation of long-term liabilities. Integrating martingale decomposition, risk-minimizing hedging, and dynamic refinancing algorithms, we formally define and eliminate a class of insurance–financial arbitrage for the first time. Results: The framework substantially reduces pricing levels for long-term products, narrows hedging errors, dampens working-capital volatility, and improves robust liability valuation and dynamic capital management under market incompleteness.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In this paper we study the pricing and hedging of nonreplicable contingent claims, such as long-term insurance contracts like variable annuities. Our approach is based on the benchmark-neutral pricing framework of Platen (2024), which differs from the classical benchmark approach by using the stock growth optimal portfolio as the numéraire. In typical settings, this choice leads to an equivalent martingale measure, the benchmark-neutral measure. The resulting prices can be significantly lower than the respective risk-neutral ones, making this approach attractive for long-term risk-management. We derive the associated risk-minimizing hedging strategy under the assumption that the contingent claim possesses a martingale decomposition. For a set of nonreplicable contingent claims, these strategies allow monitoring the working capital required to generate their payoffs and enable an assessment of the resulting diversification effects. Furthermore, an algorithmic refinancing strategy is proposed that allows modeling the working capital. Finally, insurance-finance arbitrages of the first kind are introduced and it is demonstrated that benchmark-neutral pricing effectively avoids such arbitrages.

Problem

• Pricing nonreplicable contingent claims using benchmark-neutral framework
• Deriving risk-minimizing hedging strategies for insurance products
• Avoiding insurance-finance arbitrages with benchmark-neutral pricing

Innovation

• Uses growth optimal portfolio as numéraire
• Implements risk-minimizing hedging strategy
• Proposes algorithmic refinancing for capital modeling