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We find the asymptotics of the value function maximizing the expected utilityof discounted dividend payments of an insurance company whose reserves aremodeled as a classical Cram\'er risk process, with exponentially distributedclaims, when the initial reserves tend to infinity. We focus on the power andlogarithmic utility functions. We perform some numerical analysis as well.

Asymptototic Expected Utility of Dividend Payments in a Classical Collective Risk Process