Abstract
This letter mainly investigates a general risk model with the threshold dividend strategy under assumption that the claim amounts obey a state-dependent switched exponential distribution. By establishing the differential-integral equations for the Gerber-Shiu discounted penalty function, and applying the hypergeometric functions, the closed-form absolute ruin probability is derived.
Highlights
Due to its practical importance, more and more people use the ruin probability, an important leading indicator, to judge whether an insurance company can survive or not
The classical risk model was introduced by Gerber [1]
Means the frequency of compensation. u0 represents the initial investment for an insurance company
Summary
Due to its practical importance, more and more people use the ruin probability, an important leading indicator, to judge whether an insurance company can survive or not. L. Zhao the explicit solutions of ruin time were obtained under assumption that the claim amount obeyed exponential distribution. Zhou and Guo [4] discussed the compound Poisson risk model with debit interest and dividend payments, and the explicit expressions for the Gerber-Shiu function and the optimal barrier with exponential claim amounts were given. In order to make it more general, we set the risk model with the claim sizes obeying a switched exponential distribution as follows ( ) = f x pη1e−η1x I{u≥b} + qη2e−η2x I{u
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