Stochastic control with regime switching and its applications to financial economics.

摘要

We consider problems of stochastic control with regime switching: maximization problems for stochastic models that are modulated by an observable finite-state continuous-time Markov chain. We develop the theory required to solve those problems, and we apply that theory to important problems in Financial Economics.;We present new results on the theory of classical control with regime switching, and on the theory of singular control with regime switching. We also develop the theory of impulse control with regime switching. In fact, we obtain the first version of the Hamilton-Jacobi-Bellman equation for a problem of classical stochastic control with regime switching in random time horizon and for a utility function or cost function dependent on the regime. We obtain as well the first verification theorem for a problem of stochastic impulse control with regime switching.;Furthermore, we apply our results to solve the consumption-investment problem in financial markets with regime switching, and the dividend policy problem for a company that presents business cycles. The first problem is solved explicitly, while the second problem is solved analytically for bounded dividend rates, for unbounded dividend rates and for the case in which there are dividend taxes and a fixed cost associated with each dividend payment.