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Zbl 1038.60081
Paulsen, Jostein
Optimal dividend payouts for diffusions with solvency constraints. (English)
[J] Finance Stoch. 7, No. 4, 457-473 (2003). ISSN 0949-2984; ISSN 1432-1122/e

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.
[Yuliya Mishura (Ky\"iv)]

MSC 2000:: *60J70 Appl. of diffusion theory
49K05 Free problems in one independent variable (nec./ suff.)
91B30 Risk theory etc.

Keywords: dividend payouts; diffusion models; singular control; solvency constraints; ruin probability

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Zentralblatt MATH Berlin [Germany]