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Optimum consumption and portfolio rules in a continuous-time model. (English) Zbl 1011.91502
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.”.

91G10Portfolio theory
91B16Utility theory
Full Text: DOI
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