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

TL;DR

This paper introduces a benchmark-neutral framework for pricing and hedging nonreplicable insurance claims, offering lower prices and risk management tools, while avoiding arbitrage opportunities.

Contribution

It develops a novel benchmark-neutral risk-minimization approach for nonreplicable claims, extending the classical benchmark approach with practical algorithms and arbitrage prevention.

Findings

Benchmark-neutral prices are lower than risk-neutral prices.

Hedging strategies monitor required working capital.

Arbitrage of the first kind is effectively avoided.

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 num\'eraire. 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.