Convergence to Isoelastic Utility and Policy in Multiperiod Portfolio Choice

Nils H. Hakansson

The Journal of Financial Economics, 1, September 1974, 201-224.

Abstract
This paper considers the problem of the investor who has numerous opportunities for revising his portfolio and whose choices are governed by a utility function defined on 'terminal' wealth, U₀(x₀). Attention is focused on the behavior of the induced utility functions of intermediate wealth with n periods to go, U_n(x_n), and the associated investment policies. Conditions under which the functions U_n(x_n) will tend to isoelasticity have previously been given by Mossin and by Leland. In this paper, the conditions for convergence are weakened further, to the point where they appear sufficiently board to encompass perhaps most utility functions of practical interest.

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