«Automation and Informatization of the fuel and energy complex»

Asymptotics of insurance risk for claims with "heavy tailed" distributions

UDC: 51-7(075.8)
DOI: 10.33285/2782-604X-2023-11(604)-35-40

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: classical risk model, risk function, probability of ruin, "heavy-tailed" distributions, Benktander distribution, Burr distribution, Gnedenko – Weibull distribution

Annotation:

A popular problem of the actuarial science, namely, probabilistic modeling of uncertainty in terms of the size of payments, when the latter can become big, is considered. It is known that the risk function (probability of ruin) is obtained as a solution of an integro-differential equation. Since the analytical solution of this equation is difficult, various approximations of the solution are sought. The article solved the problem of determining the asymptotic representation of the risk function in the case of "heavy tails" of well-known payout distributions. The asymptotic behavior of the risk function is found for pay-offs, modeled by Benktander distributions of types I, II, Gnedenko – Weibull and Burr type XII. A significant advantage of the derived approximations is the simplicity of the formulas of the resulting representations. The calculations were carried out under the assumption of a classical risk model for the above-mentioned "heavy tailed" distributions.

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