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MONOTONICITY PROPERTIES OF OPTIMAL INVESTMENT STRATEGIES FOR LOG‐BROWNIAN ASSET PRICES
Author(s) -
Borell Christer
Publication year - 2007
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2007.00297.x
Subject(s) - economics , geometric brownian motion , monotonic function , portfolio , mathematical economics , asset (computer security) , brownian motion , expected utility hypothesis , risk aversion (psychology) , investment (military) , econometrics , value (mathematics) , microeconomics , mathematics , financial economics , computer science , mathematical analysis , statistics , computer security , politics , political science , law , economy , diffusion process , service (business)
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.