Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy

Olena Ragulina and Jonas Šiaulys
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Olena Ragulina: Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Str. 64, 01601 Kyiv, Ukraine
Jonas Šiaulys: Institute of Mathematics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania

Mathematics, 2020, vol. 8, issue 11, 1-35

Abstract: This paper is devoted to the investigation of the ruin probability in the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. We obtain an exponential bound for the ruin probability and investigate conditions, under which it holds for a number of distributions of the premium and claim sizes. Next, we use the exponential bound to construct non-exponential bounds for the ruin probability. We show that the non-exponential bounds turn out to be tighter than the exponential one in some cases. Moreover, we derive explicit formulas for the ruin probability when the premium and claim sizes have either the hyperexponential or the Erlang distributions and apply them to investigate how tight the bounds are. To illustrate and analyze the results obtained, we give numerical examples.

Keywords: risk model; stochastic premiums; ruin probability; net profit condition; multi-layer dividend strategy; constant dividend strategy; exponential bound; non-exponential bound; integro-differential equation; hyperexponential distribution; Erlang distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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