Joint survival annuity derivative valuation in the linear-rational Wishart mortality model

Battle Count: 50

This paper is primarily focused on actuarial science and longevity/insurance risk rather than quantitative trading. However, the Wishart process framework and linear-rational modeling approach have connections to interest rate and equity derivative pricing. The risk management tools (VaR, Expected Shortfall) and approximation methods could be relevant for structured products desks dealing with longevity-linked securities. The paper's methodology is more relevant to insurance companies and pension funds than to typical quantitative trading strategies.

Implementation requires handling matrix-valued SDEs (Wishart process), solving matrix Riccati equations, computing non-central Wishart distributions, performing one-dimensional numerical integration for option pricing, and implementing three different approximation schemes. The Bru case simplifies computations significantly, but the matrix algebra (Kronecker products, spectral decompositions, matrix exponentials) adds substantial complexity. The characteristic function approach requires careful numerical integration of complex-valued functions.

The paper provides complete analytical formulas, parameter tables (Tables 1-3), and detailed proofs in the supplementary appendix. However, no code or implementation scripts are provided. The numerical experiments use specific parameter values that are fully documented, enabling reproduction of results. The Wishart process parameterization and Bru case constraints are clearly specified.