The Markovian Regime-Switching Risk Model with Constant Dividend Barrier under Absolute Ruin

Wenguang Yu, Yujuan Huang

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DOI: 10.4236/jmf.2011.13011                

Abstract

In this paper, we consider the dividend payments prior to absolute ruin in a Markovian regime-switching risk process in which the rate for the Poisson claim arrivals and the distribution of the claim amounts are driven by an underlying Markov jump process. A system of integro-differential equations with boundary conditions satisfied by the moment-generating function, the n th moment of the discounted dividend payments prior to absolute ruin and the expected discounted penalty function, given the initial environment state, are derived. Then, the matrix form of systems of integro-differential equations satisfied by the discounted penalty function are presented. Finally, we obtain the integro-differential equations satisfied by the time to reach the dividend barrier.

Keywords

Absolute Ruin, Debit Interest, Moment-Generating Function, Markovian Regime-Switching Risk Model, Dividend Barrier, Integro-Differential Equation

Conflicts of Interest

The authors declare no conflicts of interest.

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