Abstract
We consider a modification of the dividend maximization problem from ruin theory. Based on a classical risk process we 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. Furthermore, the optimal strategy identifies unfavourable surplus positions prior to ruin at which refunding is highly recommended.
Highlights
Introduction and some first considerationsIn this article we deal with an extension of the classical dividend maximization problem for an underlying classical surplus process
The problem studied there is based on a continuous sample paths process and the transaction cost parameter equals one, which results in a common single barrier type optimal strategy, both for dividends and fundings
In our contribution we introduce additional funding opportunities at random times into the classical risk model with dividends
Summary
In this article we deal with an extension of the classical dividend maximization problem for an underlying classical (compound Poisson) surplus process. The approach of interventions at the jump times of another process is related to the formulation of ruin theoretic problems under random observations Such a model comprising dividends is introduced by Albrecher et al [1] and gained some relevance in actuarial research over the last years. We need to emphasize that our present model is continuously monitored, i.e., dividend decisions can be made at any point in time and the ruin event is immediately observed Another framework where dividend maximization problems for firm value determinations play a crucial role is corporate finance. The problem studied there is based on a continuous sample paths process and the transaction cost parameter equals one, which results in a common single barrier type optimal strategy, both for dividends and fundings. Some numerical illustrations which focus on the optimal strategy as a function of the transaction cost parameter
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