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Zbl 1011.91502
Merton, Robert C.
Optimum consumption and portfolio rules in a continuous-time model.
(English)
[J] J. Econ. Theory 3, No.4, 373-413 (1971).

From the introduction: In an earlier paper [the author, Rev. Econ. Stat. 51, 247-257 (1969)], we examined the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion' hypothesis; i.e., we studied $\text{Max} E\int_0^TU(C,t) dt$. The present paper extends these results for more general utility functions, price behavior assumptions, and for income generated also from noncapital gains sources. It is shown that if the geometric Brownian motion' hypothesis is accepted, then a general separation' or mutual fund' theorem can be proved such that, in this model, the classical Tobin mean-variance rules hold without the objectionable assumptions of quadratic utility or of normality of distributions for prices.".
MSC 2000:
*91B28 Finance etc.
91B16 Utility theory

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