The investor problem based on the HJM model

TL;DR

This paper addresses a complex consumption-investment optimization problem in bond markets modeled by the HJM framework, providing solutions via HJB equations and explicit results for affine models.

Contribution

It introduces a novel approach to portfolio optimization using a general signed measure for bond maturities within the HJM model, including explicit solutions for affine cases.

Findings

Derived regularity results for the HJB solution.

Established verification theorem applicability.

Provided explicit solutions for affine HJM models.

Abstract

We consider a consumption-investment problem (both on finite and infinite time horizon) in which the investor has an access to the bond market. In our approach prices of bonds with different maturities are described by the general HJM factor model. We assume that the bond market consists of entire family of rolling bonds and the investment strategy is a general signed measure distributed on all real numbers representing time to maturity specifications for different rolling bonds. In particular, we can consider portfolio of coupon bonds. The investor's objective is to maximize time-additive utility of the consumption process. We solve the problem by means of the HJB equation for which we prove required regularity of its solution and all required estimates to ensure applicability of the verification theorem. Explicit calculations for affine models are presented.