Paper: arXiv 2212.04713

Authors: Katharina Oberpriller, Moritz Ritter, Thorsten Schmidt

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework extending insurance-finance arbitrage under model uncertainty using sets of priors and non-linear two-step evaluations. However, it is primarily theoretical and lacks empirical backtesting or real-data validation beyond illustrative pricing framework concepts.

Research Flowchart

  flowchart TD
    A["Research Goal: Define Arbitrage-Free Pricing for Hybrid Insurance under Model Uncertainty"] --> B["Inputs: Prior Sets (P), Financial Dynamics, & Doubly Stochastic Surrender/Survival Models"]
    B --> C["Methodology: Incorporate Model Uncertainty & Copula-Based Conditional Dependence"]
    C --> D["Theoretical Outcome: Introduce & Characterize 'Robust Asymptotic Insurance-Finance Arbitrage'"]
    D --> E["Evaluation Framework: Construct Non-Linear Two-Step 'QP-Evaluations'"]
    E --> F["Key Findings: QP-Evaluations Rule Out Arbitrage & Dominates All Valid Two-Step Pricing Rules"]