Igor Halperin (Fidelity): "Schrodinger Control Optimal Planning for Goal-Based Wealth Management"

Abstract: This talk addresses the problem of optimization of contributions of a financial planner such as a working individual towards a financial goal such as retirement. The objective of the planner is to find an optimal and feasible schedule of periodic installments to an investment portfolio set up towards the goal. Because portfolio returns are random, the practical version of the problem amounts to finding an optimal contribution scheme such that the goal is satisfied at a given confidence level. We suggest a semi-analytical approach to a continuous-time version of this problem based on a controlled backward Kolmogorov equation (BKE) which describes the tail probability of the terminal wealth given a contribution policy. The controlled BKE is solved semi-analytically by reducing it to a controlled Schrodinger equation and solving the latter using an algebraic method. Numerically, our approach amounts to finding semi-analytical solutions simultaneously for all values of control parameters on a small grid, and then using the standard two-dimensional spline interpolation to simultaneously represent all satisficing solutions of the original plan optimization problem. Rather than being a point in the space of control variables, satisficing solutions form continuous contour lines (efficient frontiers) in this space.

Speaker Bio: Igor Halperin is an AI researcher and a Group Data Science leader at Fidelity Investments. His research focuses on using methods of reinforcement learning, information theory, and physics for financial problems such as portfolio optimization, dynamic risk management, and inference of sequential decision-making processes of financial agents. Igor has an extensive industrial and academic experience in statistical and financial modeling, in particular in the areas of option pricing, credit portfolio risk modeling, and portfolio optimization. Prior to joining Fidelity, Igor worked as a Research Professor of Financial Machine Learning at NYU Tandon School of Engineering. Before that, Igor was an Executive Director of Quantitative Research at JPMorgan, and a quantitative researcher at Bloomberg LP. Igor has published numerous articles in finance and physics journals, and is a frequent speaker at financial conferences. He has co-authored the book “Machine Learning in Finance: From Theory to Practice” (Springer 2020), and contributed to the book “Credit Risk Frontiers” (Bloomberg LP, 2012). Igor has a Ph.D. in theoretical high energy physics from Tel Aviv University, and a M.Sc. in nuclear physics from St. Petersburg State Technical University. In February 2022, Igor was named the Buy-Side Quant of the Year by RISK magazine.