Optimal investment-consumption decisions with partially observed inflation : a discrete-time formulation

We consider a discrete-time optimal consumption and investment problem of an investor who is interested in maximizing his utility from consumption and terminal wealth subject to a random inflation in the consumption basket price over time. We consider two cases: (i) when the investor observes the basket price and (ii) when he receives only noisy signals on the basket price. We derive the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds in both cases, as it does in the continuous-time setting. The compositions of the funds in the two cases are the same but, in general, the investor’s allocations of his wealth into these funds differ.