Seminario de Probabilidad y Estadística Matemática.<br><br>PROXIMO ENCUENTRO: Miércoles 24 de Octubre, 12:00hs.<br>EXPOSITOR: Nora Muler, Universidad Torcuato Di Tella.<br>TITULO: Optimal Irreversible Switching time and dividend payment in the diffusion model.<br>
LUGAR: Departamento de Matemática, Aula de Seminarios, 2do piso, Pabellón 1.<br><br>RESUMEN: We assume that the manager of a company controls dynamically the dividend payment to the shareholders. At first, the uncontrolled reserve of the company follows a Brownian motion with drift. The manager has the possibility of switching the regime at a stopping time (called the decision time) in such a way that, from this time on, the reserve process follows one of n given Brownian motions with drift. At this stopping time the company pays (or receives) a certain amount k{i} that depends on which Brownian motion is chosen . We suppose that this decision is irreversible. The final goal is to maximize the expected discounted dividend payment until bankruptcy . We obtain the Hamilton-Jacobi-Bellman equation (HJB) associated to this problem. The HJB equation can also be interpreted as a an obstacle problem. We prove that the optimal value function is the smallest viscosity super-solution of the HJB equation (or if we think the problem as an obstacle problem, is the smallest viscosity super-solution above the obstacle). We also prove that any viscosity solution of the HJB equation that is a value function of a dividend payment strategy and a decision time is indeed the solution of the optimization problem. We show that the optimal dividend strategy depends only on the current reserve and has a "band structure".<br>
<br>As examples of this kind of problems we can think that the "decision time" is to buy another company (problem of acquisition) or that the decision time is to disinvest a branch of the company (problem of disinvestment). Joint work with Pablo Azcue.<br>
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