Optimal Expected Exponential Utility of Dividend Payments in a Brownian Risk Model
by P. Grandits, F. Hubalek, W. Schachermayer and M. Zigo
Research Reports
Number 485 (September 2006)
We consider the following optimization problem for an insurance company
$\max_{C}\mathrm{E} \left[ U\left( \int_{0}^{\infty}e^{-\beta t}dC_{t}\right)\right].$
Here $U(x)=(1-\exp(-\gamma x))/\gamma$ denotes an exponential utility function with risk aversion parameter $\gamma$, $C$ denotes the accumulated dividend process, and $\beta$ 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.
This primarily serves as Thiele Research Reports number 16-2006, but was also published in Research Reports
