Dividend optimisation: A behaviouristic approach

Abstract

In this paper, we study a dividend maximisation problem for a Brownian risk model as a surplus and a Markov-switching model describing the preference rate of an insurer. The preference rate can attain two values – a positive and a negative. The negative preference reflects the situation when the uncertainty prevails and the insurer shows more waiting tendency. In the times of the positive preference the insurer is in modus operandi.We solve the problem of finding the optimal dividend payout strategy for the setting with a classical ruin concept as well as for the case of a Parisian ruin with an exponential delay. In the first case, the optimal strategy turns out to be of a barrier type for the positive preference rate and no dividends are paid in the times of the negative rate. The optimal barrier increases with increasing intensity to switch into the state with a negative preference and shows the inverse dependence on the counterpart intensity.In the case of Parisian ruin, the optimal strategy depends on the parameter of the ruin delay and the severity of the negative preference rate. If the expected delay is relatively short the optimal strategy remains a barrier (even equal to zero) in the positive state with no dividends being paid in the negative state. If the expected delay is long, the optimal strategy in the negative state might change from not paying dividends to a band strategy.We give explicit expressions for the value functions and present conditions determining the type of the optimal strategy. Both problems are illustrated by examples.