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Utility maximization with partial information

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  • Lakner, Peter

Abstract

In the present paper we address two maximization problems: the maximization of expected total utility from consumption and the maximization of expected utility from terminal wealth. The price process of the available financial assets is assumed to satisfy a system of functional stochastic differential equations. The difference between this paper and the existing papers on the same subject is that here we require the consumption and investment processes to be adapted to the natural filtration of the price processes. This requirement means that the only available information for agents in this economy at a certain time are the prices of the financial assets up to that time. The underlying Brownian motion and the drift process in the system of equations for the asset prices are not directly observable. Particular details will be worked out for the "Bayesian" example, when the dispersion coefficient is a fixed invertible matrix and the drift vector is an Fo-measurable, unobserved random variable with known distribution.

Suggested Citation

  • Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:2:p:247-273
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    References listed on IDEAS

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    1. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
    2. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    4. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
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