Hierarchical Markov model in life insurance and social benefit schemes

Jiwook Jang, Siti Norafidah Mohd Ramli

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
76 Downloads (Pure)


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.
Original languageEnglish
Article number63
Pages (from-to)1-17
Number of pages17
Issue number3
Publication statusPublished - Sept 2018

Bibliographical note

Copyright 2018 by the authors. Licensee MDPI, Basel, Switzerland. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • life insurance
  • unemployment/disability benefits
  • retirement benefits
  • jump-diffusion process
  • hierarchical Markov process


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