Consumption and investment with interest rate risk

This paper investigates the optimal investment and consumption problem in a continuous-time financial market for agents who maximize expected power utility from consumption, facing partially hedgeable interest rate risk. With no analytic solution available for the optimal strategy, we find closed-form approximate strategies by solving the same optimization problem in two fictitious complete markets. The approximate strategies help verify the existence and the optimality of the solution to the original optimization problem and provide bounds of the optimal consumption strategy and the approximation error, both in closed form. As the interest rate increases, if the investor's risk aversion is greater than one, the wealth effect dominates the substitution effect, and consumption increases. If the risk aversion is less than one, then the substitution effect dominates, and the investor consumes less.