On a discrete interaction risk model with delayed claims and stochastic incomes under random discount rates

Yingchun Deng, Juan Liu, Ya Huang, Man Li and Jieming Zhou

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 23, 5867-5883

Abstract: In this paper, we study a discrete interaction risk model with delayed claims and stochastic incomes in the framework of the compound binomial model. A generalized Gerber-Shiu discounted penalty function is proposed to analyse this risk model in which the interest rates follow a Markov chain with finite state space. We derive an explicit expression for the generating function of this Gerber-Shiu discounted penalty function. Furthermore, we derive a recursive formula and a defective renewal equation for the original Gerber-Shiu discounted penalty function. As an application, the joint distributions of the surplus one period prior to ruin and the deficit at ruin, as well as the probabilities of ruin are obtained. Finally, some numerical illustrations from a specific example are also given.

Date: 2018
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DOI: 10.1080/03610926.2017.1406518

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