Robust asymptotic insurance-finance arbitrage

TL;DR

This paper extends the concept of insurance-finance arbitrage to account for model uncertainty, introducing a robust evaluation framework that prevents arbitrage in hybrid insurance-finance markets under uncertain dynamics.

Contribution

It develops a robust evaluation method using ${Q} ext{P}$-evaluations to characterize arbitrage absence under model uncertainty and applies it to pricing hybrid insurance products with dependence structures.

Findings

Introduction of ${Q} ext{P}$-evaluations for robust arbitrage prevention

Characterization of arbitrage absence via nonlinear evaluations

Application to pricing with copula-based dependence models

Abstract

In most cases, insurance contracts are linked to the financial markets, such as through interest rates or equity-linked insurance products. To motivate an evaluation rule in these hybrid markets, Artzner et al. (2022) introduced the notion of insurance-finance arbitrage. In this paper we extend their setting by incorporating model uncertainty. To this end, we allow statistical uncertainty in the underlying dynamics to be represented by a set of priors $\mathscr{P}$. Within this framework we introduce the notion of robust asymptotic insurance-finance arbitrage and characterize the absence of such strategies in terms of the concept of ${Q}\mathscr{P}$-evaluations. This is a nonlinear two-step evaluation which guarantees no robust asymptotic insurance-finance arbitrage. Moreover, the ${Q}\mathscr{P}$-evaluation dominates all two-step evaluations as long as we agree on the set of priors $\mathscr{P}$ which shows that those two-step evaluations do not allow for robust asymptotic insurance-finance arbitrages. Furthermore, we introduce a doubly stochastic model under uncertainty for surrender and survival. In this setting, we describe conditional dependence by means of copulas and illustrate how the ${Q}\mathscr{P}$-evaluation can be used for the pricing of hybrid insurance products.