Optimal Consumption and Investment Strategies with Stochastic Interest Rates

We study the consumption and investment choice of a time-additive power utility <p> investor and demonstrate how theinvestor should optimally hedge changes in the op- <p> portunity set. The investor is allowed to invest in stocks and interest rate dependent <p> assets in a continuous-time dynamically complete market. In particular, we demon- <p> strate that under stochastic interest rates the investor optimally hedges changes in the <p> term structure of interest rates by investing in acoupon bond, or portfolio of bonds, <p> with a payment schedule that matches the forward-expected (i.e certainty equivalent) <p> consumption pattern. This is of conceptual importance since the hedge portfolio does <p> not depend on the speci c term structure dynamics (only through the consequences <p> for the optimal consumption pattern). We consider two explicit examples where the <p> dynamics of the term structure of interest rates are given by theVasicek-model and a <p> three-factor non-Markovian Heath-Jarrow-Morton model.