We consider the problem of maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a Cram\'er risk processwith Erlang claims. We focus on the exponential claims and power and logarithmic utility functions. Finally we also analyze asymptotic behaviour of the value function  and identify the asymptotic optimal strategy. We also give the numerical procedure of finding considered value function.
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.
R
expected utility of discounted
discounted utility of
R
Cram\'er risk processwith Erlang claims. We focus on the exponential claims and power and logarithmic utility functions. Finally we also analyze asymptotic behaviour of
classical Cram\'er-Lundberg risk process. We investigate this optimization problem under the constraint that dividend rate is bounded. We prove that
A
, defined in this model, fulfills the Hamilton-Jacobi-Bellman equation
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asymptotic optimal strategy. We also give the numerical procedure of finding considered
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