On a dividend problem with random funding

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.

Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

“…Related literature. Among other papers dealing with similar topics like [17][18][19], the most related to ours is [20], which was brought to our attention only after completion of our paper. Ref.…”

Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate

“…Modeling the surplus of a company by a Brownian motion with drift, Cramér-Lundberg model or a general Lévy process, when putting constraints in the form of values at risk, time-inconsistent preferences, or incorporating random funding, these problems have been studied, for instance, in [2][3][4][5]. A general overview of the existing literature can be found in [6][7][8].…”