On the valuation of life insurance policies for dependent coupled lives

Paper: arXiv 2410.11849

Authors: Kira Henshaw, Cedric H. A. Koffi, Olivier Menoukeu Pamen, Raghid Zeineddine

Abstract

In this paper, we investigate a complex variation of the standard joint life annuity policy by introducing three distinct contingent benefits for the surviving member(s) of a couple, along with a contingent benefit for their beneficiaries if both members pass away. Our objective is to price this innovative insurance policy and analyse its sensitivity to key model parameters, particularly those related to the joint mortality framework. We employ the $QP$-rule (described in Section \ref{secgenset}), which combines the real-world probability measure $P$ for mortality risk with risk-neutral valuation under $Q$ for financial market risks. The model enables explicit pricing expressions, computed using efficient numerical methods. Our results highlight the interdependent risks faced by couples, such as broken-heart syndrome, providing valuable insights for insurers and policyholders regarding the pricing influences of these factors.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework combining Lévy processes, jump models, and joint mortality distributions under the QP-rule for exotic life insurance options. However, it lacks empirical backtesting against market dataset pricing or historical mortality claims, focusing purely on theoretical pricing derivations and parameter sensitivity.

Research Flowchart

  flowchart TD
    A[Goal: Price complex joint life annuity with contingent benefits & analyze mortality sensitivity] --> B[Inputs: Mortality risk & Financial market risk parameters]
    B --> C[Methodology: Apply QP-rule framework combining measure P and measure Q]
    C --> D[Computation: Derive explicit pricing expressions & apply efficient numerical methods]
    D --> E[Outcomes: Quantified impact of interdependent risks e.g., broken-heart syndrome on policy pricing]