This paper deals with the dividend optimization problem for a financial or an insurance entity which can control its business activities, simultaneously reducing the risk and potential profits. It also controls the timing and the amount of dividends paid out to the shareholders. The objective of the corporation is to maximize the expected total discounted dividends paid out until the time of bankruptcy. Due to the presence of a fixed transaction cost, the resulting mathematical problem becomes a mixed classical-impulse stochastic control problem. The analytical part of the solution to this problem is reduced to quasivariational inequalities for a second-order nonlinear differential equation. We solve this problem explicitly and construct the value function together with the optimal policy. We also compute the expected time between dividend payments under the optimal policy.

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We consider a consumption and investment problem where the market presents different regimes. An investor taking decisions continuously in time selects a consumption-investment policy to maximize his expected total discounted utility of consumption. The market coefficients and the investor's utility of consumption are dependent on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. We obtain explicit optimal consumption and investment policies for specific HARA utility functions. We show that the optimal policy depends on the regime. We also make an economic analysis of the solutions, and show that for every investor the optimal proportion to allocate in the risky asset is greater in a "bull market" than in a "bear market." This behavior is not affected by the investor's risk preferences. On the other hand, the optimal consumption to wealth ratio depends not only on the regime, but also on the investor's risk tolerance: high risk-averse investors will consume relatively more in a "bull market" than in a "bear market," and the opposite is true for low risk-averse investors.

We consider the problem of a Central Bank that wants the exchange rate to be as close as possible to a given target, and in order to do that uses both the interest rate level and interventions in the foreign exchange market. We model this as a mixed classical-impulse stochastic control problem, and provide for the first time a solution to that kind of problem. We give examples of solutions that allow us to perform an interesting economic analysis of the optimal strategy of the Central Bank. Copyright Blackwell Publishers, Inc..

We study the incentive effects of granting levered or unlevered stock to a risk-averse manager. The stock is granted by risk-neutral shareholders who choose leverage and compensation level. The manager applies costly effort and selects the level of volatility, both of which affect expected return. The results are driven by the attempt of the risk-neutral shareholders to maximize the value of their claims net of the compensation package. We consider a dynamic setting and find that levered stock is optimal for high-type managers, firms with high momentum, large firms, and firms for which additional volatility only implies a modest increase in expected return. JEL Classification: C61, G39