Consumption and Investment with Interest Rate Risk
26 Pages Posted: 8 Feb 2017 Last revised: 22 Jul 2018
Date Written: July 11, 2018
This paper investigates the optimal investment and consumption problem in a continuous-time financial market for investors with power utility on consumption, who face partially hedgeable interest rate risk. With no analytical solution to the optimal strategies, closed-form approximate strategies are derived by solving the same optimization problem in two fictitious complete markets. The approximate solution helps verify the existence and the optimality of the solution to the original optimization problem and provides 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 risk aversion is less than one, then the substitution effect dominates, and the investor consumes less.
Keywords: portfolio choice, consumption, stochastic interest rate, incomplete market, power utility
JEL Classification: G11, G12
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