The investor problem based on the HJM model
Volume 127 / 2021
Abstract
We consider a consumption-investment problem (both on a finite and an infinite time horizon) in which the investor has access to a 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 the whole 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 a portfolio of coupon bonds. The investor’s objective is to maximize the time-additive HARA utility of the consumption process. We solve the problem by means of the HJB equation for which we prove the required regularity of solution and all required estimates to ensure applicability of the verification theorem. Explicit calculations for affine models are presented.
