TITLE: Hereditary Portfolio Optimization with Memory

SPEAKER: Dr. Mou-Hsiung (Harry) Chang

ABSTRACT:

In this talk, we consider an infinite time horizon portfolio optimization problem in a market that consists of one savings account and one stock account whose unit price satisfies a nonlinear stochastic functional differential equation. Within the solvency region the investor is allowed to consume from the savings account and can make transactions between the two assets subject to paying capital-gain taxes as well as a fixed plus proportional transaction cost. The main objective is to seek an optimal consumption-investment strategy in order to maximize the expected utility from the total discounted consumption over the infinite time horizon. The portfolio optimization problem is formulated as a stochastic control problem that involves both the classical and impulse controls. A quasi-variational HJB inequality for the value function is derived and the verification theorem for the optimal investment consumption strategy is obtained. The value function is also shown to be the unique viscosity solution of the HJB inequality.

Bio: Dr. M. H. Chang is currently the manager of the Probability & Statistics Program and acting division chief of the Mathematical Sciences Division at the U. S. Army Research Office (ARO). Prior to joining ARO, Dr. Chang had been a tenured professor in the Department of Mathematical Sciences at the University of Alabama in Huntsville (UAH) for twenty-eight years and had served as Chair of the Mathematical Sciences Department for eight years. He received his B.S. in Applied Mathematics from National Chung-Hsing University (in Taiwan) and his M.S. and Ph.D. in Mathematics from the University of Rhode Island.

Dr. Chang publishes extensively in stochastic analysis, stochastic control, mathematical finance, and quantum Markov processes. He has published one research monograph “Stochastic Control of Hereditary Systems and Applications”, Volume 59 of the Stochastic Modeling and Applied Probability Series, Springer, New York, January 2008, ISBN 978-0-387-75805-3, more than 60 referred journal articles, and has made more than 80 invited presentations at professional conferences and universities. He is currently an associate editor for “Journal of Applied Mathematics and Stochastic Analysis” and “Stochastic Analysis and Applications”. He has also served as a referee for numerous mathematics and applied mathematics journals.