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Optimal capital growth with convex shortfall penalties

MacLean, Leonard C., Zhao, Yonggan and Ziemba, William T. (2014) Optimal capital growth with convex shortfall penalties. SRC Discussion Paper (No 15). Systemic Risk Centre, The London School of Economics and Political Science, London, UK.

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Abstract

The optimal capital growth strategy or Kelly strategy, has many desirable properties such as maximizing the asympotic long run growth of capital. However, it has considerable short run risk since the utility is logarithmic, with essentially zero Arrow-Pratt risk aversion. Most investors favor a smooth wealth path with high growth. In this paper we provide a method to obtain the maximum growth while staying above a predetermined ex-ante discrete time smooth wealth path with high probability, with shortfalls below the path penalized with a convex function of the shortfall so as to force the investor to remain above the wealth path. This results in a lower investment fraction than the Kelly strategy with less risk, and lower but maximal growth rate under the assumptions. A mixture model with Markov transitions between several normally distributed market regimes is used for the dynamics of asset prices. The investment model allows the determination of the optimal constrained growth wagers at discrete points in time in an attempt to stay above the ex-ante path.

Item Type: Monograph (Discussion Paper)
Official URL: http://www.systemicrisk.ac.uk/
Additional Information: © Leonard C. MacLean, Yonggan Zhao, William T. Ziemba submitted 2014
Divisions: Systemic Risk Centre
Subjects: H Social Sciences > HB Economic Theory
Sets: Research centres and groups > Systemic Risk Centre
Date Deposited: 29 Aug 2014 10:59
Last Modified: 20 Feb 2019 03:47
Projects: ES/K002309/1
Funders: Economic and Social Research Council
URI: http://eprints.lse.ac.uk/id/eprint/59292

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