Optimal dividend payouts for diffusions with solvency constraints (Q1424720)

This paper is concerned with the classical problem of optimal dividend payouts for a company. The author considers a company where surplus follows a diffusion process and whose objective is to maximize expected discounted dividend payouts to the shareholders, more exactly, to find a payout-scheme that maximizes the expected present value of all payouts until ruin occurs. The following restrictions are imposed: no dividends are allowed to be paid out unless surplus is at least \(b_0\), and the surplus immediately after payment cannot be below \(b_0\). Also, there is a level \(b^*\) so that whenever surplus goes above \(b^*\), the excess is paid out as dividends. If \(b_0>b^*\), it is shown that an optimal restricted policy is to use a barrier strategy at \(b_0\). This barrier is such that the probability of negative surplus within time \(T\) does not exceed prescribed \(\varepsilon>0\). It is discussed how this \(b_0\) can be calculated and a complete treatment is given when the surplus follows a Brownian motion with drift.