Optimal Consumption and Portfolio Decisions with Partially Observed Real Prices

33 Pages Posted: 30 Apr 2007 Last revised: 13 Apr 2009

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management; Hong Kong Polytechnic University - Faculty of Business; Ajou University

Jussi Keppo

National University of Singapore - NUS Business School

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

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Abstract

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.

Keywords: Optimal Consumption and Investment, Inflation, Stochastic Control with partial observations, Separation Principle, Zakai Equation

JEL Classification: C61, D83, G11,D11, D91

Suggested Citation

Bensoussan, Alain and Keppo, Jussi and Sethi, Suresh, Optimal Consumption and Portfolio Decisions with Partially Observed Real Prices. Mathematical Finance, Vol. 19, No. 2, pp. 215-236, 2009. Available at SSRN: https://ssrn.com/abstract=983450

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 West Campbell Rd
SM 30
Richardson, TX 75080-3021
United States
9728836117 (Phone)

HOME PAGE: http://www.utdallas.edu/~axb046100/

Hong Kong Polytechnic University - Faculty of Business

Dept SEEM
Systems Engr * Engr Mgmt
Hong Kong, Hong Kong
China

Ajou University ( email )

Ajou
France

Jussi Keppo (Contact Author)

National University of Singapore - NUS Business School ( email )

1 Business Link
Singapore, 117592
Singapore

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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