Simple approximations for the ruin probability in the risk model with stochastic premiums and a constant dividend strategy
Volume 7, Issue 3 (2020), pp. 245–265
Pub. online: 4 August 2020
Type: Research Article
Open Access
Open Access
Received
12 March 2020
12 March 2020
Revised
29 May 2020
29 May 2020
Accepted
10 July 2020
10 July 2020
Published
4 August 2020
4 August 2020
Abstract
We deal with a generalization of the risk model with stochastic premiums where dividends are paid according to a constant dividend strategy and consider heuristic approximations for the ruin probability. To be more precise, we construct five- and three-moment analogues to the De Vylder approximation. To this end, we obtain an explicit formula for the ruin probability in the case of exponentially distributed premium and claim sizes. Finally, we analyze the accuracy of the approximations for some typical distributions of premium and claim sizes using statistical estimates obtained by the Monte Carlo methods.
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