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Abstract
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We consider optimal consumption and portfolio investment problems of an
investor who is interested in maximizing his utilities 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 observations 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. 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 will differ. However, in the particular case when the
investor has CRRA utility, his optimal investment allocations into these funds
are also the same in both cases.
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