Mathematical Sciences Department Financial Math Seminar
Bahman Angoshtari, University of Miami
Monday, April 7th
11:00am - 12:00 pm
Title: Predictable Forward Performance Processes for Loss-Averse Agents
Abstract: Predictable forward performance processes (PFPPs) are stochastic optimal control frameworks for an agent who controls a randomly evolving system but can only prescribe the system dynamics for a short period ahead. This is a common scenario in which a controlling agent frequently re-calibrates her model. In this talk, I discuss a new class of PFPPs for loss-averse agents who update their loss threshold and loss-aversion level throughout their investment horizon. Construction of these loss-averse PFPPs reduces to solving a sequence of inverse optimal control problems, in which the value function is known and a (linear-concave) utility function is to be found. Existence and uniqueness results for the inverse problems are obtained by the analysis of a corresponding Fredholm integral equation. Illustrative numerical examples are provided in the context of conditionally complete Black-Scholes model. This is joint work with Shida Duan and Thaleia Zariphopoulou.