Risk Sensitive Portfolio Management with Cox--Ingersoll--Ross Interest Rates: The HJB Equation

This paper presents an application of risk sensitive control theory in financial decision making. The investor has an infinite horizon objective that can be interpreted as maximizing the portfolio’s risk adjusted exponential growth rate. There are two assets, a stock and a bank account, and two underlying Brownian motions, so this model is incomplete. The novel feature here is that the interest rate for the bank account is governed by Cox-Ingersoll-Ross dynamics. This is significant for risk sensitive portfolio management because the factor process, unlike in the Gaussian and all other cases treated in the literature, cannot be negative.