Universal Journal of Accounting and Finance Vol. 9(5), pp. 927 - 934
DOI: 10.13189/ujaf.2021.090504
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Simulation for Ruin Probabilities in Insurance with Sequence Markov Dependence Random Variables

Quang Phung Duy ^1,*, Thinh Nguyen Huu ¹, Chien Doan Quyet ^2
1 Mathematics Department, Foreign Trade University, Hanoi, Viet Nam
² Statistics & Actuarial Science, Soongsil University, Seoul, South Korea

ABSTRACT

The aim of this paper is to calculate ruin probabilities using Monte Carlo method for two models: i) classical risk model with claim amounts are homogeneous Markov chains; ii) generalized risk models with premiums amounts, claim amounts are homogeneous Markov chains. The sequence of random variables in the article is considered as a series of Markov dependent random variables. The main results of this paper are Lemma 3.1, Lemma 3.2 and Lemma 3.3, which have built mathematical formulas for the simulation of the probability of insurance models considered in this paper. From those lemmas, we build algorithms to simulate ruin probability for insurance models considered in this paper. From these algorithms, we build numerical results illustrating the problems posed in the paper. These results all show that when the initial capital increases, the ruin probability will decrease, and when the time increases, the ruin probability will increase. This result is consistent with the theory of the risk problem in insurance.

KEYWORDS
Ruin Probability, Homogeneous Markov Chain, Monte Carlo Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Quang Phung Duy , Thinh Nguyen Huu , Chien Doan Quyet , "Simulation for Ruin Probabilities in Insurance with Sequence Markov Dependence Random Variables," Universal Journal of Accounting and Finance, Vol. 9, No. 5, pp. 927 - 934, 2021. DOI: 10.13189/ujaf.2021.090504.

(b). APA Format:
Quang Phung Duy , Thinh Nguyen Huu , Chien Doan Quyet (2021). Simulation for Ruin Probabilities in Insurance with Sequence Markov Dependence Random Variables. Universal Journal of Accounting and Finance, 9(5), 927 - 934. DOI: 10.13189/ujaf.2021.090504.