Stochastic Mortality Model with Fractional Lévy Dynamics

Battle Count: 85

The paper is primarily focused on actuarial science and longevity risk management rather than quantitative trading. However, it is relevant to longevity-linked derivatives pricing (longevity swaps, corridors, caplets), which are traded instruments. The SVD approximation methodology and fractional process modeling techniques could be adapted for other derivative pricing problems. The paper's contribution to understanding long-range dependence in mortality data has implications for pension fund management and insurance-linked securities.

The paper involves advanced mathematical concepts including fractional Lévy processes, Volterra integral representations, singular value decomposition of integral operators, Esscher and Girsanov transforms, and Fourier inversion for derivative pricing. The numerical implementation requires careful handling of the non-Markovian structure, causal masking of SVD approximations, and residual correction schemes. The calibration involves constrained optimization over multiple Lévy specifications. The theoretical framework spans stochastic analysis, functional analysis, and actuarial mathematics.

The paper provides detailed mathematical derivations, parameter values for numerical tests, and calibration methodology. However, no code repository is mentioned. The empirical calibration uses publicly available Human Mortality Database data for France. The SVD implementation details are described in Appendix N with diagrams. Reproduction would require implementing the fractional Lévy process, SVD lifting, and residual correction from scratch.