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Optimal consumption with stochastic prices in continuous time

Published online by Cambridge University Press:  14 July 2016

T. Björk ,
J. Myhrman  and
M. Persson
T. Björk*
Affiliation:
Royal Institute of Technology, Stockholm
J. Myhrman*
Affiliation:
Stockholm School of Economics
M. Persson*
Affiliation:
Stockholm School of Economics
*
∗Postal address: Optimization and Systems Theory, Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden.
∗Postal address: Stockholm School of Economics, Box 6501, S-113 83 Stockholm, Sweden.
∗Postal address: Stockholm School of Economics, Box 6501, S-113 83 Stockholm, Sweden.
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Abstract

In this paper we consider an economic agent (the consumer) having initial wealth x(0), which he is allowed to spend during the time interval [0, T]. There are N consumer goods, the prices of which are described by a system of stochastic differential equations, and the consumer can spend his money as he pleases provided that he does not get into debt. The consumer's problem is to maximize his expected utility over [0, T]. Given a separable utility function we show that the optimal consumption policy is linear in the wealth variable regardless of the structure of the price system, and if we assume that the price processes are geometric Brownian motions we can give the optimal consumption policy explicitly.

Keywords

STOCHASTIC CONTROLMATHEMATICAL ECONOMICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 35 - 47
Copyright
Copyright © Applied Probability Trust 1987 

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References

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