Stochastic mortality model with respect to mixed fractional Poisson process: Calibration and empirical analysis of long-range dependence in actuarial valuation

Abstract

Recently, many studies have adopted the fractional stochastic mortality process in characterising the long-range dependence (LRD) feature of mortality dynamics, while there are still fewer appropriate non-Gaussian fractional models to describe it. We propose a stochastic mortality process driven by a mixture of Brownian motion and modified fractional Poisson process to capture the LRD of mortality rates. The survival probability under this new stochastic mortality model keeps flexibility and consistency with existing affine-form mortality models, which makes the model convenient in evaluating mortality-linked products under the market-consistent method. The formula of survival probability also considers the historical information from survival data, which enables the model to capture historical health records of lives. The LRD feature is reflected by our proposed model in the empirical analysis, which includes the calibration and prediction of survival curves based on recent generation data in Japan and the UK. Finally, the consequent empirical analysis of annuity pricing illustrates the difference of whether this feature is involved in actuarial valuation.