A risk model with paying dividends and random environment

Bara Kim, Hwa-Sung Kim and Jeongsim Kim

Insurance: Mathematics and Economics, 2008, vol. 42, issue 2, 717-726

Abstract: We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:42:y:2008:i:2:p:717-726

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