Author(s)

Wenguang Yu, Yujuan Huang

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In this paper, we study the dividend payments prior to absolute ruin in a Markov-dependent risk process in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. A system of integro-differential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to absolute ruin and the discounted penalty function, given the initial environment state, are derived. In the two-state risk model, explicit solutions to the integro-differential equations satisfied by the nth moment of the discounted dividend payments prior to absolute ruin are obtained when the claim size distribution is exponentially distributed. Finally, the matrix form of systems of integro-differential equations satisfied by the discounted penalty function are presented.

Absolute Ruin, Markov-Dependent Insurance Risk Model, Debit Interest, Moment-Generating Function

W. Yu and Y. Huang, "Dividend Payments and Related Problems in a Markov-Dependent Insurance Risk Model under Absolute Ruin," American Journal of Industrial and Business Management, Vol. 1 No. 1, 2011, pp. 1-9. doi: 10.4236/ajibm.2011.11001.