Optimal Consumption and Portfolio Decisions with Partially Observable Real Prices

Mathematical Finance, 19(2), April 2009, 215-236

33 Pages Posted: 17 Jun 2020

See all articles by Alain Bensoussan

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management

Jussi Keppo

National University of Singapore (NUS) - NUS Business School

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: 2009

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 constant relative risk-aversion (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, M11, M20

Suggested Citation

Bensoussan, Alain and Keppo, Jussi and Sethi, Suresh, Optimal Consumption and Portfolio Decisions with Partially Observable Real Prices (2009). Mathematical Finance, 19(2), April 2009, 215-236, Available at SSRN: https://ssrn.com/abstract=3607974

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/

Jussi Keppo

National University of Singapore (NUS) - NUS Business School ( email )

Mochtar Riady Building
15 Kent Ridge Drive
Singapore, 119245
Singapore

HOME PAGE: http://https://www.jussikeppo.com

Suresh Sethi (Contact Author)

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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