Suboptimal Control of Dividends under Exponential Utility

We consider an insurance company modelling its surplus process by a Brownian motion with drift. Our target is to maximise the expected exponential utility of discounted dividend payments, given that the dividend rates are... [ view full abstract ]

We consider an insurance company modelling its surplus process by a Brownian motion with drift. Our target is to maximise the expected exponential utility of discounted dividend payments, given that the dividend rates are bounded by some constant.

Numerical and theoretical considerations lead us to the conclusion that the optimal strategy must be of a barrier type. That is why, we cannot apply the methods used in the classical case. 

Our approach estimates the distance between the performance function corresponding to a non-optimal strategy to the value function. Also, we investigate the two most obvious suboptimal strategies: constant and barrier-type.