# New Representation for Non Ruin Probability of Insurance Model with Rent Contracts and Its Application for Assessment of Critical Risks

## Keywords:

Insurance, rent, regular variation, heavy traffic, critical risks, integrodifferential equation## Abstract

The paper considers the particular solution of one integro-differential equation of insurance risk theory. New representation for that solution is found, which is used for assessment of critical risks of the insurance companies that conduct purely rent operations. The critical risks are found in the case of a heavy traffic and regular tail variation of the insurance premiums distribution function.

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*Mathematical Problems of Computer Science*,

*36*, 70–78. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/268

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