The risk model with stochastic premiums, dependence and a threshold dividend strategy

Ragulina, Olena

doi:10.15559/17-VMSTA89

Modern Stochastics: Theory and Applications

The risk model with stochastic premiums, dependence and a threshold dividend strategy

Volume 4, Issue 4 (2017), pp. 315–351

Olena Ragulina

https://doi.org/10.15559/17-VMSTA89

Pub. online: 8 December 2017 Type: Research Article

Open Access

Received
4 September 2017

Revised
21 October 2017

Accepted
8 November 2017

Published
8 December 2017

Abstract

The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by Farlie–Gumbel–Morgenstern copulas. In addition, dividends are paid to its shareholders according to a threshold dividend strategy. We derive integral and integro-differential equations for the Gerber–Shiu function and the expected discounted dividend payments until ruin. Next, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes. In particular, we find explicit formulas for the ruin probability in the model without either dividend payments or dependence as well as for the expected discounted dividend payments in the model without dependence. Finally, numerical illustrations are presented.

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Keywords

Risk model with stochastic premiums Farlie–Gumbel–Morgenstern copula threshold strategy Gerber–Shiu function expected discounted dividend payments ruin probability integro-differential equation

MSC2010

91B30 60G55 62P05

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