Optimal expected exponential utility of dividend payments in a Brownian risk model

Peter Grandits, Friedrich Hubalek, Walter Schachermayer and Mislav Žigo

Scandinavian Actuarial Journal, 2007, vol. 2007, issue 2, 73-107

Abstract: We consider the following optimisation problem for an insurance company Here U(x) = (1−exp(−γx))/γ denotes an exponential utility function with risk aversion parameter γ, C denotes the accumulated dividend process, and β a discount factor. We show that – assuming that a certain integral equation has a solution – the optimal strategy is a barrier strategy. The barrier function is a solution of the integral equation and turns out to be time-dependent. In addition, we study the problem from a different point of view, namely by using a certain ansatz for the value function and the barrier.

Date: 2007
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DOI: 10.1080/03461230601165201

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