MONOTONICITY PROPERTIES OF OPTIMAL INVESTMENT STRATEGIES FOR LOG‐BROWNIAN ASSET PRICES

Christer Borell

Mathematical Finance, 2007, vol. 17, issue 1, 143-153

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.

Date: 2007
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