Journal article

Moments of the Dividend Payments and Related Problems in a Markov-Modulated Risk Model

S Li, Y Lu

North American Actuarial Journal | Published : 2007

Abstract

In this paper we derive some results on the dividend payments prior to ruin in a Markovmodulated risk process in which the rate for the Poisson claim arrival process and the distribution of the claim sizes vary in time depending on the state of an underlying (external) Markov jump process (J(t); t ≥ 0). The main feature of the model is the flexibility in modeling the arrival process in the sense that periods with very frequent arrivals and periods with very few arrivals may alternate, and that the states of (J(t); t ≥ 0) could describe, for example, epidemic types in health insurance or weather conditions in car insurance. A system of integro-differential equations with boundary conditions s..

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