Institute of Robotics and Automatic Information System
Seminar Series：Advanced Robotics & MEMS
报告人： Ruihua Liu
Department of Mathematics University of Dayton, Ohio.
题目：Apply Stochastic Optimal Control to Investment and Consumption with Regime-Switching and Transaction Cost
摘要：In this presentation we apply the stochastic control method to study an infinitehorizon problem of optimal investment and consumption with proportional transaction costs in continuous-time regime-switching models. An investor distributes his/her wealth between a risky asset (a stock) and a risk-less asset (a bond) and consumes at a non-negative rate from the bond account. The market parameters (the interest rate, the appreciation rate and the volatility rate of the stock) are assumed to depend on a continuous-time Markov chain with finite number of states (also known as regimes). The objective of the optimization problem is to maximize the expected discounted total utility of consumption. For this optimal control problem, the Hamilton-Jacobi-Bellman (HJB) equation is given by a system of m0 coupled variational equalities where m0 is the total number of regimes. For a class of HARA (hyperbolic absolute risk aversion) type utility functions, we establish some fundamental properties of the value function and show that the value function is a viscosity solution of the HJB equation. We then treat a power utility function and derive qualitative properties of the optimal trading strategy and the value function.
Ruihua Liu, Tenured Associate Professor, Department of Mathematics, University of Dayton, Ohio. Ph.D., August 2001, Applied Mathematics University of Georgia, Advisor: Qing Zhang, Dissertation Title: Control and Filtering of Stochastic Markovian Systems. His RESEARCH INTERESTS include Financial Mathematics and Computational Finance, Stochastic Optimal Control and Applications, Applied Stochastic Analysis.