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We consider the problem of maximizing the discounted utility of dividendpayments of an insurance company whose reserves are modeled as a classicalCram\'er-Lundberg risk process. We investigate this optimization problem underthe constraint that dividend rate is bounded. We prove that the value functionfulfills the Hamilton-Jacobi-Bellman equation and we identify the optimaldividend strategy.

Optimizing expected utility of dividend payments for a Cram\'er-Lundberg risk proces