Paper: arXiv 2602.06415

Authors: Jose Da Fonseca, Patrick Wong

Abstract

This study proposes a linear-rational joint survival mortality model based on the Wishart process. The Wishart process, which is a stochastic continuous matrix affine process, allows for a general dependency between the mortality intensities that are constructed to be positive. Using the linear-rational framework along with the Wishart process as state variable, we derive a closed-form expression for the joint survival annuity, as well as the guaranteed joint survival annuity option. Exploiting our parameterisation of the Wishart process, we explicit the distribution of the mortality intensities and their dependency. We provide the distribution (density and cumulative distribution) of the joint survival annuity. We also develop some polynomial expansions for the underlying state variable that lead to fast and accurate approximations for the guaranteed joint survival annuity option. These polynomial expansions also significantly simplify the implementation of the model. Overall, the linear-rational Wishart mortality model provides a flexible and unified framework for modelling and managing joint mortality risk.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically sophisticated linear-rational Wishart mortality model to solve the joint survival derivative option pricing problem. While it presents strong analytical derivations, closed-form expressions, and polynomial approximations, it relies primarily on synthetic numerical experiments rather than robust empirical backtesting on actual demographic/market datasets.

Research Flowchart

  flowchart TD
    A[Goal: Value Joint Survival Annuities <br>& Manage Joint Mortality Risk] --> B[Inputs: Wishart Process as State Variable <br>& Linear-Rational Framework]
    B --> C[Methodology: Model Mortality Intensities <br>& Dependencies via Matrix Affine Process]
    C --> D[Derivations & Expansions: Closed-Form Solutions <br>& Polynomial Expansions]
    D --> E[Outcomes: Explicit Density/CDF of Joint Annuity <br>& Fast/Accurate Option Pricing]

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0 of 121 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.