Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions

Nils H. Hakansson

Econometrica, 38, September 1970, 587-607; reprinted in Stochastic Optimization Models in Finance (eds. W. T. Ziemba and R. G. Vickson), Academic Press, 1975, 525-545.

This paper develops a sequential model of the individualís economic decision problem under risk. On the basis of this model, optimal consumption, investment, and borrowing-lending strategies are obtained in closed form for a class of utility functions. For a subset of this class the optimal consumption strategy satisfies the permanent income hypothesis precisely. The optimal investment strategies have the property that the optimal mix of risky investments is independent of wealth, noncapital income, age, and impatience to consume. Necessary and sufficient conditions for long-run capital growth are also given.

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