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Risks 2018, 6(3), 63; https://doi.org/10.3390/risks6030063

Hierarchical Markov Model in Life Insurance and Social Benefit Schemes

1
Department of Actuarial Studies and Business Analytics, Faculty of Business and Economics, Macquarie University, Sydney 2109, Australia
2
School of Mathematical Sciences, Faculty of Science and Technology, National University of Malaysia, Bandar Baru Bangi 43600, Malaysia
*
Author to whom correspondence should be addressed.
Received: 29 April 2018 / Revised: 5 June 2018 / Accepted: 18 June 2018 / Published: 25 June 2018
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Abstract

We explored the effect of the jump-diffusion process on a social benefit scheme consisting of life insurance, unemployment/disability benefits, and retirement benefits. To do so, we used a four-state Markov chain with multiple decrements. Assuming independent state-wise intensities taking the form of a jump-diffusion process and deterministic interest rates, we evaluated the prospective reserves for this scheme in which the individual is employed at inception. We then numerically demonstrated the state of the reserves for the scheme under jump-diffusion and non-jump-diffusion settings. By decomposing the reserve equation into five components, our numerical illustration indicated that an extension of the retirement age has a spillover effect that would increase government expenses for other social insurance programs. We also conducted sensitivity analyses and examined the total-reserves components by changing the relevant parameters of the transition intensities, which are the average jump-size parameter, average jump frequency, and diffusion parameters of the chosen states, with figures provided. Our computation revealed that the total reserve is most sensitive to changes in average jump frequency. View Full-Text
Keywords: life insurance; unemployment/disability benefits; retirement benefits; jump-diffusion process; hierarchical Markov process life insurance; unemployment/disability benefits; retirement benefits; jump-diffusion process; hierarchical Markov process
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Jang, J.; Mohd Ramli, S.N. Hierarchical Markov Model in Life Insurance and Social Benefit Schemes. Risks 2018, 6, 63.

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