Doctoral School Mathematics and Scientific Computing

Abstract: We consider a modification of the dividend maximization problem from ruin theory. Beside the classical dividend control, we introduce an additional funding opportunity into the model. The task is to maximize the difference of expected cumulated discounted dividends and total expected discounted additional funding (subject to some proportional transaction costs). For modelling dividends we use the common approach whereas for the funding opportunity we use the jump times of another independent Poisson process at which we choose an appropriate funding height. In case of exponentially distributed claims we are able to determine an explicit solution to the problem and derive an optimal strategy whose nature heavily depends on the size of the transaction costs.[hide abstract]