# M. E. Taylor Analysis and PDE Seminar – Paul Smith (Kaizen Technologies)

## November 13 @ 3:30 pm - 4:30 pm

**Topics in quantitative finance and the application of Markov Decision Processes**

**Abstract.** Quantitative hedge funds seek to apply scientific, mathematical, and statistical methods to the investment process so as to maximize risk-adjusted returns under certain constraints. In this talk, we begin with a brief overview of three major necessary components to consider in any such process: (1) “alpha research”, (2) portfolio construction, and (3) order execution. After laying the groundwork, we introduce an optimization problem for a stochastic system motivated by the goal of maximizing portfolio return in the presence of transaction costs given a predictive signal. We present results in a constrained setting of AR(1) signals with restricted cross-correlation structure and portfolio controls. Key to the result is establishing a suitable expected survival time, which relies upon an approximation argument and a priori bounds to establish a contraction mapping. Finally, we discuss extensions of this result, viewing the problem as a certain average cost Markov Decision Problem. This is ongoing joint work with Chutian Ma.