Several topics will be presented in this talk. In the first part, we consider some portfolio optimization problems with stochastic dividends, stochastic volatility or delays. The Hamilton-Jacobi-Bellman (HJB) equations are derived, which are second order nonlinear PDEs. We then establish the existence results of the HJB equations and prove the verification theorems. In the second part, we consider the portfolio optimization based on financial data. In particular, we derive an explicit formula for the optimal investment strategy for Black-Litterman Model with Conditional Value-at-Risk (CVaR). In the third part, we develop an efficient and robust tail-based normal approximation method for CVaR evaluation. The method works very well especially for financial data set of small size.

Short Bio: Tao Pang is currently an associate professor of mathematics and the interim director of the Financial Mathematics Program at NC State University. Tao Pang came to NC State University in 2002, after he got his PhD of Applied Mathematics from Brown University. His research interests include stochastic control, portfolio optimization, financial data analysis and computational finance. He has directed 7 PhD students, and has 2 current PhD students. Tao Pang has published more than 30 papers on both journals on mathematics and journals on finance. One of his papers won the Best Paper Prize of SIAM Journal on Control and Optimization (SICON) in 2011. He has been invited to give more than 40 presentations at conferences and seminars. He is a Chartered Financial Analyst (CFA) and certified Financial Risk Manager (FRM). Tao Pang is the co-founder of the NC Chapter of Global Association of Risk Professionals (GARP), and served as the chapter co-director from 2011 to 2016. He also has many years of volunteer-based public service and administration experience.

Prof. Tao Pang is a candidate for the Director of Financial Mathematics position.