We consider a firm that simultaneously controls its risk and dividend policies. However, a reduction in risk generates a reduction in its potential profits. The management also decides the times and the amount of dividends to be paid out to the shareholders, taking into account that there are fixed costs and taxes associated with each dividend payment. We present a survey that shows how the methods of mixed classical-impulse stochastic control can be applied to model and solve these problems. We also present some open problems.
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