In the framework of the intertemporal asset allocation problem, this dissertation focuses on the modelling of inflation risk and its impact on intertemporal asset allocation strategies. The contributions of this dissertation to the current literature are as follows.

First, in considering inflation risk, Merton's continuous-time framework of the intertemporal model is extended to accommodate a time-varying consumption price index. Recall that it is important to consider a time-varying consumption price index for the intertemporal asset allocation problem because: (i) a time-varying price level will affect consumption decisions since agents care about how many goods they can consume (real terms) instead of how much money they spend for consumption. (ii) A time-varying price level will affect the portfolio strategies because the implied inflation risk from the time-varying price index affects interest rates (bond yields) of different maturities.

Second, this dissertation extends the solution method of the intertemporal asset allocation problem, that is, the method of dynamic programming, to a framework with a stochastic consumption price level. An analytical solution formula is provided for the optimal intertemporal investment strategy in this extended framework by using the Feymann-Kac formula.

With regard to inflation modelling, the third contribution of this work is to develop a new interest rate model to include inflation-indexed bonds. Based on this new model, we can study the hedging performance of inflation-indexed bonds against the inflation risk within the intertemporal asset allocation problem.

Fourthly, due to the difficulty in solving the intertemporal asset allocation problem for some extended cases, this dissertation develops a computational algorithm based on the Jacobi iteration method in the Markov Chain Approximation family of Kushner (1977). This algorithm is then applied to our intertemporal asset allocation problem taking account of various kinds of short-sale constraints.