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Monotonicity Properties Of Optimal Investment Strategies For Log‐Brownian Asset Prices

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  • Christer Borell

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.

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  • Christer Borell, 2007. "Monotonicity Properties Of Optimal Investment Strategies For Log‐Brownian Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 143-153, January.
    • Handle: RePEc:bla:mathfi:v:17:y:2007:i:1:p:143-153
    DOI: 10.1111/j.1467-9965.2007.00297.x
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    Cited by:

    1. Dejian Tian & Weidong Tian, 2016. "Comparative statics under κ-ambiguity for log-Brownian asset prices," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 361-378, December.
    2. Tianxiao Wang, 2012. "Risk minimizing of derivatives via dynamic g-expectation and related topics," Papers 1208.2068, arXiv.org.
    3. Lijun Bo & Yijie Huang & Xiang Yu, 2023. "An extended Merton problem with relaxed benchmark tracking," Papers 2304.10802, arXiv.org, revised Mar 2024.

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