Paper: arXiv 2510.06698

Authors: Raquel M. Gaspar, Thorsten Schmidt

Abstract

To make medium- and long-term insurance products attractive, it is essential to enable participation in stock market returns. However, to eliminate downside risk, guarantees must be included, which naturally leads to the challenge of valuing such contracts within a unified insurance-finance framework. We develop a general setup that allows for the joint modelling of financial markets, mortality and policyholder behaviour. Within this framework, we propose a general affine approach and derive explicit valuation formulas for variable annuities and related contracts, while retaining computational tractability due to the affine structure. The model permits flexible dependence between mortality and equity dynamics, as supported by empirical evidence from the COVID-19 pandemic. Moreover, surrender intensities are modelled as functions of the underlying affine process, thereby introducing market dependence into lapse behaviour. The resulting framework combines analytical tractability with sufficient flexibility to capture key features of long-term insurance products.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using enlargement of filtrations and affine processes to value variable annuities under market-dependent mortality and lapse risks. While mathematically sophisticated and novel in its unified insurance-finance arbitrage-free approach, it relies purely on theoretical derivations with minimal empirical validation in the provided text.

Research Flowchart

  flowchart TD
    A["Research Goal: Valuing Insurance Products with Guarantees in a Unified Framework"] --> B["Inputs: Financial Markets, Mortality & Market-Dependent Surrender Dynamics"]
    B --> C["Framework: Joint Affine Process Modeling"]
    C --> D["Computational Engine: Characteristic Functions & Affine Riccati System"]
    D --> E["Key Outcome: Explicit Analytical Pricing Formulas for Variable Annuities"]