Qingshuo Song : Solving a class of time-inconsistent problems

Posted by Jie Yang , part of the Statistics and Data Science Seminar.

At

Oct. 7, 2020, 4 p.m.

In

Zoom

Abstract

The characterization of the efficient frontier in Markowitz portfolio optimization is to minimize a linear combination of mean and variance of the terminal stock price. Such a problem is known as the time-inconsistent optimization and the main difficulty is due to the failure of the dynamic programming principle. The existing approaches are game-theoretic framework and decoupling techniques on its FBSDE formulation. In this talk, we will discuss an alternative approach. The key observation is to identify the linear-quadratic structure of the underlying optimization as a function of probability distribution. This leads to explicit solutions of a class of master equations, which provides the optimal strategy to a class of time-inconsistent optimizations. Some extensions to partially observed systems will be considered briefly if time is permitted. The discussion is based on a manuscript available at https://arxiv.org/pdf/1910.05236.pdf.