Hansjoerg Albrecher (Université de Lausanne)

Optimal ratcheting of dividends in insurance

Abstract: In this talk, we give an overview of recent developments in identifying optimal dividend payment strategies for an insurance company, when the dividend rate is not allowed to decrease. The optimality criterion here is to maximize the expected value of the aggregate discounted dividend payments up to the time of ruin. In the framework of the classical risk model and its Brownian approximation, the solution of the corresponding two-dimensional optimal control problem is presented and optimal strategies are numerically determined for several concrete examples. The implementations illustrate that the restriction of ratcheting does not lead to a large efficiency loss when compared to the classical un-constrained optimal dividend strategy. We also consider an extension of the results to drawdown constraints on the dividend rate, where a curious square-root rule emerges. Finally, we discuss optimal dividends for a risk model where claims occur according to a shot-noise Cox process, which can be the situation of an insurance company exposed to natural catastrophe risks. We show that the resulting two-dimensional control problem can be tackled by similar means, and that the additional uncertainty of the claim arrival process can in fact be an advantage for shareholders when an appropriate dividend payout strategy is implemented.