Optimal consumption and investment strategies with stochastic interest rates

We characterize the solution to the consumption and investment problem of a timeadditive power utility investor in a continuous-time dynamically complete market with stochastic changes in the opportunity set. It is demonstrated that under stochastic interest rates the investor optimally hedges against changes in the term structure of interest rates by investing in a coupon bond, or portfolio of bonds, with a payment schedule that matches the forward-expected (i.e. certainty equivalent) consumption pattern. This is of conceptual importance since the hedge portfolio only depends on the specific term structure dynamics through the consequences for the optimal consumption pattern. We consider two explicit examples where the term structure dynamics are given by the Vasicek-model and a three-factor non-Markovian HeathJarrow-Morton model.