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

Abstract EN

This paper studied an asset and liability management problem with stochastic interest rate, where interestrate is assumed to be governed by an affine interest rate model, while liability process is driven by the driftedBrownian motion.

The investors wish to look for an optimal investment strategy to maximize the expected utilityof the terminal surplus under hyperbolic absolute risk aversion (HARA) utility function, which consists of powerutility, exponential utility, and logarithm utility as special cases.

By applying dynamic programming principleand Legendre transform, the explicit solutions for HARA utility are achieved successfully and some special casesare also discussed.

Finally, a numerical example is provided to illustrate our results.