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The Kelly growth optimal strategy with a stop-loss rule. (English) Zbl 1423.91007

From the Introduction: “The plan of the paper is as follows. Section 2 provides some background, and section 3 reviews the HJB for the investment problem and introduces notation. In section 4 we derive a non-linear PDE for the optimal strategy, and in section 5 we consider a few examples with known solutions and discuss to what extent the equation can be applied. In section 6, we provide a numerical solution for the Kelly strategy subject to a periodically reset stop-loss rule. Section 7 concludes.”
Reviewer’s comment: The article is written very carelessly. Abbreviations are not explained. I did not find anything new in this article.

MSC:

91G10 Portfolio theory
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
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References:

[1] DOI: 10.1239/aap/1029955147 · Zbl 0963.91053 · doi:10.1239/aap/1029955147
[2] Browne, S., Can you do better than Kelly in the short run? InFinding the Edge: Mathematical Analysis of Casino Games, edited by O. Vancura, J. Cornelius, W.R. Eadington, pp. 215–231, 2000a (Institute for the Study of Gambling and Commercial Gaming, University of Nevada: Reno).
[3] DOI: 10.1007/978-1-4757-2435-6_3 · doi:10.1007/978-1-4757-2435-6_3
[4] DOI: 10.1111/j.1467-9965.1993.tb00044.x · Zbl 0884.90031 · doi:10.1111/j.1467-9965.1993.tb00044.x
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