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A risk model with paying dividends and random environment |
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| Authors: | Bara Kim Jeongsim Kim |
| Institution: | a Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Republic of Korea b Department of Business Administration, Kwangwoon University, Wolgye-dong, Nowon-ku, Seoul, 139-701, Republic of Korea c Department of Mathematics Education, Chungbuk National University, 12, Gaeshin-dong, Heungduk-ku, Cheongju, Chungbuk, 361-763, Republic of Korea |
| 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. |
| Keywords: | IM13 |
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