Mathematics – Probability
Scientific paper
2005-03-24
Annals of Applied Probability 2004, Vol. 14, No. 4, 1810-1837
Mathematics
Probability
Published at http://dx.doi.org/10.1214/105051604000000909 in the Annals of Applied Probability (http://www.imstat.org/aap/) by
Scientific paper
10.1214/105051604000000909
We study a model of a corporation which has the possibility to choose various production/business policies with different expected profits and risks. In the model there are restrictions on the dividend distribution rates as well as restrictions on the risk the company can undertake. The objective is to maximize the expected present value of the total dividend distributions. We outline the corresponding Hamilton-Jacobi-Bellman equation, compute explicitly the optimal return function and determine the optimal policy. As a consequence of these results, the way the dividend rate and business constraints affect the optimal policy is revealed. In particular, we show that under certain relationships between the constraints and the exogenous parameters of the random processes that govern the returns, some business activities might be redundant, that is, under the optimal policy they will never be used in any scenario.
Choulli Tahir
Taksar Michael
Zhou Xun Yu
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