We describe a novel approach to the study of multi-period portfolio selection problems with time varying alphas, trading costs, and constraints. We show that, to each multi-period portfolio optimization problem, one may associate a “dual” Bayesian dynamic model. The dual model is constructed so that the most likely sequence of hidden states is the trading path which optimizes expected utility of the portfolio. The existence of such a model has numerous implications, both theoretical and computational. Sophisticated computational tools developed for Bayesian state estimation can be brought to bear on the problem, and the intuitive theoretical structure attained by recasting the problem as a hidden state estimation problem allows for easy generalization to other problems in finance. Time permitting, we discuss several applications to this approach.
This is joint work with Gordon Ritter.
Petter Kolm, Director of the Mathematics in Finance Masters Program and ClinicalProfessor, Courant Institute of Mathematical Sciences, New York University
Petter Kolm is the Director of the Mathematics in Finance Masters Program and Clinical Associate Professor at the Courant Institute of Mathematical Sciences, New York University and the Principal of the Heimdall Group, LLC. Previously, Petter worked in the Quantitative Strategies Group at Goldman Sachs Asset Management where his responsibilities included researching and developing new quantitative investment strategies for the group's hedge fund. Petter coauthored the books Financial Modeling of the Equity Market: From CAPM to Cointegration (Wiley, 2006), Trends in Quantitative Finance (CFA Research Institute, 2006), Robust Portfolio Management and Optimization (Wiley, 2007), and Quantitative Equity Investing: Techniques and Strategies (Wiley, 2010). He holds a Ph.D. in mathematics from Yale, an M.Phil. in applied mathematics from Royal Institute of Technology, and an M.S. in mathematics from ETH Zurich.
Petter is a member of the editorial boards of the International Journal of Portfolio Analysis and Management (IJPAM), Journal of Investment Strategies (JOIS), Journal of Portfolio Management (JPM), and the board of directors of the International Association for Quantitative Finance (IAQF). As a consultant and expert witness, he has provided his services in areas such as algorithmic and quantitative trading strategies, econometrics, forecasting models, portfolio construction methodologies incorporating transaction costs, and risk management procedures.