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Optimal dividend payouts for diffusions with solvency constraints. (English) Zbl 1038.60081
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 ε>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.

60J70Applications of Brownian motions and diffusion theory
49K05Free problems in one independent variable (optimality conditions)
91B30Risk theory, insurance