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

Paper: arXiv 2506.19494

Authors: Michael Schmutz, Eckhard Platen, Thorsten Schmidt

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework for benchmark-neutral risk-minimization in long-term nonreplicable insurance claims using stochastic calculus and martingale decompositions. However, it lacks empirical backtesting or real-world data validation, remaining purely theoretical in its present form.

Research Flowchart

  flowchart TD
    A[Goal: Pricing & Hedging Nonreplicable Long-Term Claims] --> B[Inputs: Stock Growth Optimal Portfolio as Numéraire & Claim Inputs]
    B --> C[Framework: Platen Benchmark-Neutral Pricing]
    C --> D[Method: Martingale Decomposition for Risk-Minimizing Hedging]
    D --> E[Process: Algorithmic Refinancing & Working Capital Modeling]
    E --> F[Outcomes: Lower Long-Term Prices, Working Capital Diversification, & Avoidance of Insurance-Finance Arbitrage]