On a discrete interaction risk model with delayed claims and stochastic incomes under random discount rates |
| |
Authors: | Yingchun Deng Juan Liu Man Li Jieming Zhou |
| |
Institution: | 1. Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, China;2. School of Business, Hunan Normal University, Changsha, China |
| |
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. |
| |
Keywords: | Delayed claims Discrete risk model Gerber-Shiu discounted penalty function Markov chain Random discount rates Stochastic incomes |
|
|