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OPTIMAL CONSUMPTION AND PORTFOLIO DECISIONS WITH PARTIALLY OBSERVED REAL PRICES
Author(s) -
Bensoussan Alain,
Keppo Jussi,
Sethi Suresh P.
Publication year - 2009
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2009.00362.x
Subject(s) - economics , consumption (sociology) , portfolio , investment (military) , mutual fund separation theorem , microeconomics , inflation (cosmology) , constant (computer programming) , econometrics , monetary economics , financial economics , computer science , social science , sociology , politics , political science , law , programming language , physics , theoretical physics
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 constant relative risk‐aversion (CRRA) utility, his optimal investment allocations into these funds are also the same in both cases.