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Survival probabilities in a discrete semi-Markov risk model

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  • Chen, Mi
  • Yuen, Kam Chuen
  • Guo, Junyi

Abstract

In this paper, we consider the survival probability for a discrete semi-Markov risk model, which assumes individual claims are influenced by a Markov chain with finite state space and there is autocorrelation among consecutive claim sizes. Our semi-Markov risk model is similar to the one studied in Reinhard and Snoussi (2001,2002) [1,2] without the restriction imposed on the distributions of the claims. In particular, the model of study includes several existing risk models such as the compound binomial model (with time-correlated claims) and the compound Markov binomial model (with time-correlated claims) as special cases. The main purpose of the paper is to develop a recursive method for computing the survival probability in the two-state model, and present some numerical examples to illustrate the application of our results.

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  • Chen, Mi & Yuen, Kam Chuen & Guo, Junyi, 2014. "Survival probabilities in a discrete semi-Markov risk model," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 205-215.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:205-215
    DOI: 10.1016/j.amc.2014.01.057
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    1. F. Baltazar-Larios & Luz Judith R. Esparza, 2022. "Statistical Inference for Partially Observed Markov-Modulated Diffusion Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 571-593, June.
    2. Palmowski, Zbigniew & Ramsden, Lewis & Papaioannou, Apostolos D., 2024. "Gerber-Shiu theory for discrete risk processes in a regime switching environment," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    3. Zhou, Zhongbao & Xiao, Helu & Deng, Yingchun, 2015. "Markov-dependent risk model with multi-layer dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 273-286.
    4. Jingchao Li & Bihao Su & Zhenghong Wei & Ciyu Nie, 2022. "A Multinomial Approximation Approach for the Finite Time Survival Probability Under the Markov-modulated Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2169-2194, September.
    5. Bihao Su & Chenglong Xu & Jingchao Li, 2022. "A Deep Neural Network Approach to Solving for Seal’s Type Partial Integro-Differential Equation," Mathematics, MDPI, vol. 10(9), pages 1-21, May.

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