Optimal Dividend Policies (Part I)

Prof. Halil Soner

ETH Zürich

About the Speaker

Soner is currently a Professor at the Swiss Federal Institute of Technology in Zurich, Eidgenössische Technische Hochschule Zürich (ETH-Z) and also holds a senior chair at the Swiss Finance Institute. His research is on nonlinear analysis with emphasis on optimal stochastic control, partial differential equations, stochastic processes and mathematical finance.

Prior to moving to Zurich, he has spent nine years in Istanbul, Turkey and nineteen years in the United States of America. During his tenure in Turkey, he held the Isik Inselbag Chair at Sabanci University for two years and was a member of the Mathematics Department at Koc University for seven years prior to that. He has received his doctoral degree from the Division of Applied Mathematics of Brown University. Later, he was a member of the Department of Mathematical Sciences at Carnegie Mellon 1986 - 1998. In 1998, he became the Paul M. Wyhtes '55 Professor of Engineering and Finance at Princeton.

He has co-authored a book, with Wendell Fleming, on viscosity solutions and stochastic control; Controlled Markov Processes and Viscosity Solutions, and authored or co-authored several articles on nonlinear partial differential equations, viscosity solutions, stochastic optimal control and mathematical finance. Since 2011, he has been the Executive Secretary of the Bachelier Finance Society and in 2014 he was awarded the Alexander von Humboldt Research Award.

Abstract

This classical problem is to design an optimal dividend payment scheme that maximizes the expected discounted dividend payments until bankruptcy. The cash flow of the company is modelled as continuous diffusion process with a given positive mean rate. It is well known this is also the classical De Finetti problem in insurance with cash flows as jump processes.

The initial paper of Jeanblanc and Shiryayev formulates this problem as a singular optimal control problem. Then, the solution is obtained explicitly through a threshold policy. Namely, the company pays dividends only when the cash level is above an optimal threshold. There has been many generalisations of this problem.

In these talks, I will describe the problems and its extensions in detail.