Fractional models in longevity risk modelling and management.

Dr. Zhehao Zhang (XJTLU)

Date: Wednesday, 11th February 2026 at 2pm 

Title: Fractional models in longevity risk modelling and management.

Abstract: Population ageing intensifies longevity risk faced by pension funds and life insurers, yet the long‑range dependence (LRD) observed in mortality dynamics is still insufficiently incorporated into actuarial models and risk management. This talk presents fractional stochastic mortality frameworks for longevity risk modelling and management. We first model mortality intensity using mixed fractional Brownian motion with jumps to capture LRD, mortality shocks, and population basis risk, while retaining an affine‑form survival probability under a no‑strong‑arbitrage pricing framework, enabling tractable pricing, sensitivity analysis, and dynamic hedging of longevity‑linked products. We then introduce a non‑Gaussian fractional mortality model driven by a mixture of Brownian motion and a modified fractional Poisson process, which preserves analytical tractability, incorporates historical survival information, and remains consistent with market‑consistent valuation methods. Empirical evidence from UK and Japan data demonstrates that fractional models better capture LRD in mortality dynamics, leading to materially different survival projections, annuity prices, and hedging performance, highlighting the importance of incorporating LRD in longevity risk modelling and management.