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Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion. (English) Zbl 1183.91077

Summary: In the absence of dividends, the surplus of an insurance company is modeled by a compound Poisson process perturbed by diffusion. Dividends are paid at a constant rate whenever the modified surplus is above the threshold, otherwise no dividends are paid. Two integro-differential equations for the expected discounted dividend payments prior to ruin are derived and closed-form solutions are given. Accordingly, the Gerber-Shiu expected discounted penalty function and some ruin related functionals, the probability of ultimate ruin, the time of ruin and the surplus before ruin and the deficit at ruin, are considered and their analytic expressions are given by general solution formulas. Finally the moment-generating function of the total discounted dividends until ruin is discussed.

MSC:

91B30 Risk theory, insurance (MSC2010)
45J05 Integro-ordinary differential equations
60K05 Renewal theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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