Author: Borell, Christer

Source: Mathematical Finance, Volume 17, Number 1, January 2007 , pp. 143-153(11)

Publisher: Wiley-Blackwell

Abstract:

Consider the geometric Brownian motion market model and an investor who strives to maximize expected utility from terminal wealth. If the investor's relative risk aversion is an increasing function of wealth, the main result in this paper proves that the optimal demand in terms of the total wealth invested in a given risky portfolio at any date is decreasing in absolute value with wealth. The proof depends on the functional form of the Brunn-Minkowski inequality due to Prékopa.

Keywords: log-Brownian asset prices; portfolio; wealth; risk aversion

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9965.2007.00297.x

Affiliations: 1: Chalmers University of Technology and Göteborg University, Sweden

Publication date: 2007-01-01

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