# THE RESULTS OF INTEGRAL OPERATION IN A RISK MODEL WITH EXCESS OF LOSS REINSURANCE

### Abstract

This article considers a discrete time insurance risk model. The premiums are assumed a constant and are calculated according to the expected value principle. The claims process are assumed to be independent sequences of indentically distributed non-negative random variables. The risk model includes the excess of loss reinsurance contract effect to the surplus process. An integral operation was established. Using the integral operation, the ruin probability of the insurance at period n is calculated by ruin probability at the first period. The fixed points of the integral operation are shown.

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*UTEHY Journal of Science and Technology*,

*36*, 84-88. Retrieved from https://tapchi.utehy.edu.vn/index.php/jst/article/view/577