Finite Time Ruin Probability in the Collective Risk Model using Continuous Time Markov Chain

Bazyari, Abouzar

Volume 9, Issue 4 (12-2023) mmr 2023, 9(4): 24-48 | Back to browse issues page

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Bazyari A. Finite Time Ruin Probability in the Collective Risk Model using Continuous Time Markov Chain. mmr 2023; 9 (4) :24-48
URL: http://mmr.khu.ac.ir/article-1-3269-en.html

Finite Time Ruin Probability in the Collective Risk Model using Continuous Time Markov Chain

Abouzar Bazyari

Department of Statistics, Persian Gulf University, Bushehr, Iran , ab_bazyari@yahoo.com

Abstract: (770 Views)

The ability of insurers to pay claims is one of the most important issues in the management of insurance companies. In this paper, the collective risk model of insurance company with constant premium and compound Poisson process over a period of time is considered. For a general class of claim sizes with light tailed and heavy tailed distributions, a formula for computing the finite time ruin probability is obtained using the probability transformation, then the matrix form of the presented formula by the transformation matrix and continuous time Markov chain generating matrix is rewritten. Also, using simulation paths from the risk process for claim sizes with Exponential, Normal and Pareto distributions with different values of initial reserve at the different times, in addition to compute the finite time ruin probabilities and unbiased confidence intervals, their values estimated for transformation matrix and Markov chain generating matrix.

Keywords: Collective risk model, Continuous time Markov process, Finite time ruin probability, Probability transformation, Risk process.

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