A Multinomial Approximation Approach for the Finite Time Survival Probability Under the Markov-modulated Risk Model

Jingchao Li (), Bihao Su, Zhenghong Wei and Ciyu Nie
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Jingchao Li: Shenzhen University
Bihao Su: Shanghai University of Finance and Economics
Zhenghong Wei: Shenzhen University
Ciyu Nie: Nanyang Technological University

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 2169-2194

Abstract: Abstract In this paper, we consider the problem of computing different types of finite time survival probabilities for a Markov-Modulated risk model and a Markov-Modulated risk model with reinsurance, both with varying premium rates. We use the multinomial approximation scheme to derive an efficient recursive algorithm to compute finite time survival probabilities and finite time draw-down survival probabilities. Numerical results show that by comparing with MCMC approximation, discretize approximation and diffusion approximation methods, the proposed scheme performs accurate results in all the considered cases and with better computation efficiency.

Keywords: Finite time survival probability; Multinomial approximation; Markov-modulated risk model; Draw-down time; Reinsurance (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09897-z

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