Robust asymptotic insurance-finance arbitrage

This paper studies the valuation of insurance contracts linked to financial markets, for example through interest rates or in equity-linked insurance products. We build upon the concept of insurance-finance arbitrage as introduced by Artzner et al. (Math Financ, 2024), extending their work by incorporating model uncertainty. This is achieved by introducing statistical uncertainty in the underlying dynamics to be represented by a set of priors \({{\mathscr {P}}}\). Within this framework we propose the notion of robust asymptotic insurance-finance arbitrage (RIFA) and characterize the absence of such strategies in terms of the new concept of \({Q}{{\mathscr {P}}}\)-evaluations. This nonlinear two-step evaluation ensures absence of RIFA. Moreover, it dominates all two-step evaluations, as long as we agree on the set of priors \({{\mathscr {P}}}\). Our analysis highlights the role of \({Q}{{\mathscr {P}}}\)-evaluations in terms of showing that all two-step evaluations are free of RIFA. Furthermore, we introduce a doubly stochastic model to address uncertainty for surrender and survival, utilizing copulas to define conditional dependence. This setting illustrates how the \({Q}{{\mathscr {P}}}\)-evaluation can be applied for the pricing of hybrid insurance products, highlighting the flexibility and potential of the proposed approach.