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Optimal dividend strategies in a Cramér-Lundberg model with capital injections. (English) Zbl 1189.91075
Summary: We consider a classical risk model with dividend payments and capital injections. Thereby, the surplus has to stay positive. Like in the classical de Finetti problem, we want to maximize the discounted dividend payments minus the penalized discounted capital injections. We derive the Hamilton-Jacobi-Bellman equation for the problem and show that the optimal strategy is a barrier strategy. We explicitly characterize when the optimal barrier is at 0 and find the solution for exponentially distributed claim sizes.

MSC:
91B30 Risk theory, insurance (MSC2010)
91G80 Financial applications of other theories
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