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Optimal dividend and capital injection strategies with transaction costs and exponentially distributed observation time. (English) Zbl 1299.91083
Summary: In this paper, we consider the optimal joint dividend and capital injection strategies with proportional and fixed costs. It supposes that capitals can be injected whenever they are profitable, but dividends can only be paid at the arrival times of a Poisson process with intensity $$\gamma>0$$. Our objective is to determine an optimal strategy of maximizing that the expected cumulative discounted dividends minus the expected discounted costs of capital injections before bankruptcy. By solving some impulse control problems, we get the closed-form solutions depending on the parameters of model.
##### MSC:
 91B30 Risk theory, insurance (MSC2010)