Optimizing expected utility of dividend payments for a Cram\'er-Lundberg risk proces
We consider the problem of maximizing the discounted utility of dividend payments of an insurance company whose reserves are modeled as a classical Cram\'er-Lundberg risk process. We investigate this optimization problem under the constraint that dividend rate is bounded. We prove that the value function, defined in this model, fulfills the Hamilton-Jacobi-Bellman equation and identify the optimal dividend strategy. Eventually we extend our results for the reserve process modeled as a classical Cram\'er-Lundberg risk process with capital injections. For the extended model we also prove some results regarding asymptotic analysis of the value function.
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- Hubalek, Friedrich & Schachermayer, Walter, 2004. "Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 193-225, April.
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