Title:Functional Ito’s Formula and Stochastic Portfolio Optimization with Delays
Speaker:Professor Tao Pang， North Carolina State University
We consider a stochastic portfolio optimization model in which the returns of risky asset depend on its past performance. The price of the risky asset is described by a stochastic delay differential equation. The investor’s goal is to maximize the expected discounted utility by choosing optimal investment and consumption as controls. We use the functional Ito’s formula to derive the associated Hamilton-Jacobi-Bellman equation. For logarithmic and exponential utility functions, we can obtain explicit solutions in a finite dimensional space.