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Risks 2019, 7(1), 17; https://doi.org/10.3390/risks7010017

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

1
Department of Mathematics, Aarhus University, 8000 Aarhus, Denmark
2
Institut de Science Financière et d’Assurances, Université Lyon 1, 69007 Lyon, France
3
Department of Statistics & Actuarial Science, Hong Kong University, Hong Kong 999077, China
*
Author to whom correspondence should be addressed.
Received: 11 December 2018 / Revised: 31 January 2019 / Accepted: 4 February 2019 / Published: 11 February 2019
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Abstract

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. In the first part of this paper, fitting of PH distributions to human lifetimes is considered. The class of generalized Coxian distributions is given special attention. In part, some new software is developed. In the second part, 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. View Full-Text
Keywords: generalized Coxian distribution; EM algorithm, guaranteed minimum death benefit; high-water benefit; jump diffusion, matrix-analytic methods; reserves; Wiener-Hopf factorization generalized Coxian distribution; EM algorithm, guaranteed minimum death benefit; high-water benefit; jump diffusion, matrix-analytic methods; reserves; Wiener-Hopf factorization
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Asmussen, S.; Laub, P.J.; Yang, H. Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits. Risks 2019, 7, 17.

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