Adaptive control of three continuous-time portfolio and consumption models

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.This research was partially supported by NSF Grant No. ECS-84-03286-A01 and by University of Kansas General Research Allocation No. 3806-XO-0038.