On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income

Wenguang Yu

doi:10.1155/2013/320146

Abstract

We consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function. In particular, the discount interest force process is also regulated by the Markovian regime-switching process. Applications of the integral equations are given to be the Laplace transform of the time of ruin, the deficit at ruin, and the surplus immediately before ruin occurs. For exponential distribution, the explicit expressions for these quantities are obtained. Finally, a numerical example is also given to illustrate the effect of the related parameters on these quantities.

Highlights

In recent years, ruin theory under regime-switching model is becoming a popular topic
The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function
We consider the case that the claim amounts and premium numbers are exponentially distributed

Summary

Introduction

Ruin theory under regime-switching model is becoming a popular topic This model is proposed in Reinhard [1] and Asmussen [2]. Many papers on ruin probabilities and the expected discounted penalty function under the Markovian regime-switching risk model have been published. Some works in this area include Ng and Yang [3], Li and Lu [4], Lu and Li [5], Zhang [6], Zhu and Yang [7, 8], Yu [9], Dong et al [10], Wei et al [11], Elliott et al [12], Ma et al [13], Dong and Liu [14], Mo and Yang [15], Zhang and Siu [16], Li and Ren [17], and the references therein

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