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On Risk Model with Dividends Payments Perturbed by a Brownian Motion – An Algorithmic Approach

Published online by Cambridge University Press:  17 April 2015

Esther Frostig
Esther Frostig*
Affiliation:
Department of Statistics, University of Haifa, Haifa, Israel
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Abstract

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Assume that an insurance company pays dividends to its shareholders whenever the surplus process is above a given threshold. In this paper we study the expected amount of dividends paid, and the expected time to ruin in the compound Poisson risk process perturbed by a Brownian motion. Two models are considered: In the first one the insurance company pays whatever amount exceeds a given level b as dividends to its shareholders. In the second model, the company starts to pay dividends at a given rate, smaller than the premium rate, whenever the surplus up-crosses the level b. The dividends are paid until the surplus down-crosses the level a, a < b . We assume that the claim sizes are phase-type distributed. In the analysis we apply the multidimensional Wald martingale, and the multidimensional Asmussesn and Kella martingale.

Keywords

Wald martingalestopping timeoptional sampling theoremKella and Whitt martingale
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 1 , May 2008 , pp. 183 - 206
Copyright
Copyright © ASTIN Bulletin 2008

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