Portfolio Selection with Liability and Affine Interest Rate in the HARA Utility Framework

Abstract

This paper studied an asset and liability management problem with stochastic interest rate, where interest rate is assumed to be governed by an affine interest rate model, while liability process is driven by the drifted Brownian motion. The investors wish to look for an optimal investment strategy to maximize the expected utility of the terminal surplus under hyperbolic absolute risk aversion (HARA) utility function, which consists of power utility, exponential utility, and logarithm utility as special cases. By applying dynamic programming principle and Legendre transform, the explicit solutions for HARA utility are achieved successfully and some special cases are also discussed. Finally, a numerical example is provided to illustrate our results.