Adaptive control of three continuous-time portfolio and consumption models

  • T. E. Duncan
  • B. Pasik-Duncan
Contributed Papers


An economic application of adaptive control is presented using three continuous time portfolio and consumption models that are natural generalizations of a model of Merton. In these models of the wealth of an individual investor, it is assumed that the various parameters are deterministic functions of time or stochastic processes. An adaptive control problem arises for each of these models when it is assumed that the average return rate of the risky asset, which is either a deterministic function or a stochastic process, is not observed. For these models, a recursive family of estimators of the average return rate of the risky asset is given based on the observations of the wealth. These estimates are used in the control of the wealth equation.

Key Words

Adaptive control recursive parameter estimators continuous-time portfolio and consumption models stochastic optimal control 


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    Merton, R. C.,Optimum Consumption and Portfolio Rules in a Continuous-Time Model, Journal of Economic Theory, Vol. 3, pp. 373–413, 1971.Google Scholar
  2. 2.
    Duncan, T. E., andPasik-Duncan, B.,Adaptive Control of a Continuous-Time Portfolio and Consumption Model, Journal of Optimization Theory and Applications, Vol. 61, pp. 47–52, 1989.Google Scholar
  3. 3.
    Fleming, W. H., andRishel, R. W.,Deterministic and Stochastic Optimal Control, Springer, Berlin, Germany, 1975.Google Scholar
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    Doob, J. L.,Stochastic Processes, Wiley, New York, New York, 1953.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • T. E. Duncan
    • 1
  • B. Pasik-Duncan
    • 1
  1. 1.Department of MathematicsUniversity of KansasLawrence

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