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Ruin Probabilities in the Insurance Individual Risk Model with Probability Transition Matrix of Interest Rate
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Abouzar Bazyari *   |
| Department of Statistics, Persian Gulf University, Bushehr, Iran. |
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Abstract: (67 Views) |
| Insurance companies are modeled with mathematical and statistical models in terms of their random structure. In this paper, the individual risk model of insurance company with different interest rates in a period of time is considered and assumed that the interest rates have the probability transition matrix with finite and countable state. The finite and infinite time ruin probabilities are computed using the conditional probability on the first claim of density function. Moreover, the upper bounds for the infinite time ruin probability are obtained using the mathematical induction. In the numerical examples, the ruin probabilities for heavy tailed distributions are compared with the obtained probabilities in Bazyari (2022) for the classical individual risk model and also, the infinite time ruin probabilities for light tailed distributions are compared with Lundberg's inequality. The results show that the existence of interest rate with probability transition matrix and having finite state leads to decrease the ruin probabilities. |
Article number: 3 |
| Keywords: Conditional probability, Lundberg inequality, Pareto distribution, Probability transition matrix, Ruin probability |
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Full-Text [PDF 203 kb]
(60 Downloads)
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Type of Study: Research |
Subject:
Special
Received: 2024/01/29 | Accepted: 2024/10/4 | Published: 2025/01/17
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