[Todos] Seminario de Probabilidad y Estadística Matemática

[Pablo Groisman]

Seminario de Probabilidad y Estadística Matemática.

PROXIMO ENCUENTRO: Miércoles 24 de Octubre, 12:00hs.
EXPOSITOR: Nora Muler, Universidad Torcuato Di Tella.
TITULO: Optimal Irreversible Switching time and dividend payment in the
diffusion model.
LUGAR: Departamento de Matemática, Aula de Seminarios, 2do piso, Pabellón 1.

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".

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.

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