Seminars & Colloquia Calendar
When is the dual utility optimizer a martingale?
Kimberly Weston - Rutgers University
Location: Hill 705
Date & time: Thursday, 11 April 2019 at 2:00PM - 3:00PM
Abstract: In this talk, I will discuss a decades-old question related to the utility maximization problem. The utility maximization problem is the prototypical concave stochastic control problem in mathematical finance. This concave optimization problem has a convex dual problem whose domain ranges over a class of supermartingales. We would like to know when the dual optimizer is a martingale and not just a supermartingale. We provide general conditions on the input parameters that guarantee the martingale property for the dual optimizer. The conditions are related to the BMO theory of martingales and Muckenhoupt's (Ap) condition. We also construct a counterexample, which shows that our general conditions are in some sense optimal because any lessening of our conditions delivers a dual optimal supermartingale.
This is joint work with Dmitry Kramkov.