Event Type:

Probability Seminar

Date/Time:

Tuesday, March 8, 2016 - 16:00 to 17:00

Location:

WNGR 201

Guest Speaker:

Institution:

Oregon State University

Abstract:

In this talk, we will introduce a classical optimization problem in insurance, called optimal dividend strategies. The problem was first considered by Bruno De Finetti in 1957, and it had been intensively studied to this day. In the past, the researchers developed several types of dividend strategies which maximize the expectation of total discounted dividends. One of these, called the barrier type fascinates me. The diffusion approximation model for surplus process was proved to have the optimality of barrier strategy under some technical conditions. Later, the optimal barrier strategy was proved possible for the compound Poisson case (Gerber and Shiu 2006). However the remarkable results (Loeffen 2008, Kyprianou 2010) for general negative spectrally Levy process provide the sufficient conditions of optimality for barrier strategy. Specifically, the scale functions for a Levy process should be convex beyond some point, or Levy measure should be log-convex. This was later extended further to other cases like refracted Levy processes. Recently, there had been a rising interest in the models whose discounting factor (interest rate) evolves as a classical stochastic process. The result of Eisenberg 2015 in this regard will be discussed, and two simple extensions and open questions will be given.