Optimal implementation delay of taxation with trade-off for spectrally negative Lévy risk processes

Abstract

In this paper we consider two cases of optimal implementation delay of taxation with trade-off under spectrally negative Lévy insurance risk processes. In the first case, we assume that the insurance company starts to pay tax only when its surplus level reaches a certain level, and at the termination time of the business there is a terminal value incurred to the company. A method is developed to determine the optimal starting-tax surplus level at which the total expected discounted value of all tax payments up to the termination time plus the discounted terminal value is maximized. In the second case, the company still pays tax subject to a starting-tax surplus level, but with capital inject..