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Stochastic mortality dynamics driven by mixed fractional Brownian motion

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  • Zhou, Hongjuan
  • Zhou, Kenneth Q.
  • Li, Xianping

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.

Suggested Citation

  • Zhou, Hongjuan & Zhou, Kenneth Q. & Li, Xianping, 2022. "Stochastic mortality dynamics driven by mixed fractional Brownian motion," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 218-238.
    • Handle: RePEc:eee:insuma:v:106:y:2022:i:c:p:218-238
    DOI: 10.1016/j.insmatheco.2022.07.006
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    More about this item

    Keywords

    Stochastic mortality modeling; Long-range dependence; Directional derivative; Mortality sensitivity; Natural hedging;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts

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