Stochastic mortality dynamics driven by mixed fractional Brownian motion

Abstract

Recently, the long-range dependence (LRD) of mortality dynamics has been identified and studied in the actuarial literature. The non-Markovian feature caused by LRD can raise new challenges in actuarial valuation and risk management. This paper proposes a new modeling approach that uses a combination of independent Brownian motion and fractional Brownian motion to achieve a flexible setting on capturing the LRD in mortality dynamics. The closed-form solutions of survival probabilities are derived for valuation and hedging purposes. To obtain mortality sensitivity measures in the presence of LRD, we develop a novel derivation method using directional derivatives. Our method is flexible in the sense that it can not only reflect the effect of LRD on mortality sensitivities, but also include some existing sensitivity measures as a special case. Finally, we provide a numerical illustration to analyze the performance of different sensitivity measures in a natural hedge of mortality risk.