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Stochastic mortality models: an infinite-dimensional approach

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  • Stefan Tappe
  • Stefan Weber

Abstract

Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite-dimensional) Wiener process and a compensated Poisson random measure. A major innovation of the paper is the introduction of a family of processes called forward mortality improvements which provide a flexible tool for a simple construction of stochastic forward mortality models. In practice, the notion of mortality improvements is a convenient device for the quantification of changes in mortality rates over time, and enables, for example, the detection of cohort effects. We show that the forward mortality rates satisfy Heath–Jarrow–Morton-type consistency conditions which translate to conditions on the forward mortality improvements. While the consistency conditions for the forward mortality rates are analogous to the classical conditions in the context of bond markets, the conditions for the forward mortality improvements possess a different structure. Forward mortality models include a cohort parameter besides the time horizon, and these two dimensions are coupled in the dynamics of consistent models of forward mortality improvements. In order to obtain a unified framework, we transform the systems of Itô processes which describe the forward mortality rates and improvements. In contrast to term structure models, the corresponding stochastic partial differential equations (SPDEs) describe the random dynamics of two-dimensional surfaces rather than curves. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Stefan Tappe & Stefan Weber, 2014. "Stochastic mortality models: an infinite-dimensional approach," Finance and Stochastics, Springer, vol. 18(1), pages 209-248, January.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:1:p:209-248
    DOI: 10.1007/s00780-013-0219-2
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    References listed on IDEAS

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    Cited by:

    1. Stefan Tappe, 2019. "Existence of affine realizations for stochastic partial differential equations driven by L\'evy processes," Papers 1907.00335, arXiv.org.
    2. Claudio Fontana & Eckhard Platen & Stefan Tappe, 2024. "Real-world models for multiple term structures: a unifying HJM framework," Papers 2411.01983, arXiv.org.
    3. Marcus Christiansen & Andreas Niemeyer, 2015. "On the forward rate concept in multi-state life insurance," Finance and Stochastics, Springer, vol. 19(2), pages 295-327, April.
    4. Stefan Tappe, 2022. "Invariant cones for jump-diffusions in infinite dimensions," Papers 2206.13913, arXiv.org, revised Nov 2023.

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    More about this item

    Keywords

    Mortality; Longevity; Forward mortality; Heath–Jarrow–Morton; Mortality improvements; Dynamic point processes; Stochastic partial differential equations (SPDEs); 97M30; 60H15; G22; J11;
    All these keywords.

    JEL classification:

    • 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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