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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