Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits

Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits

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Phase-type (PH) distributions are defined as distributions of lifetimes of finite continuous-time Markov processes. Their traditional applications are in queueing, insurance risk, and reliability, but more recently, also in finance and, though to a lesser extent, to life and health insurance. The advantage is that PH distributions form a dense class and that problems having explicit solutions for exponential distributions typically become computationally tractable under PH assumptions. The fitting of PH distributions to human lifetimes is considered, and some new software is developed. The pricing of life insurance products such as guaranteed minimum death benefit and high-water benefit is treated for the case where the lifetime distribution is approximated by a PH distribution and the underlying asset price process is described by a jump diffusion with PH jumps. The expressions are typically explicit in terms of matrix-exponentials involving two matrices closely related to the Wiener-Hopf factorization, for which recently, a Lévy process version has been developed for a PH horizon. The computational power of the method of the approach is illustrated via a number of numerical examples.

[1] Asmussen, S., Laub, P.J. and Yang, H. (2019), “Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits.” Risks, vol. 7(1), 17, pp. 1-22.

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