Relative growth optimal strategies in an asset market game

Yaroslav Drokin () and Mikhail Zhitlukhin ()
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Yaroslav Drokin: National Research University Higher School of Economics
Mikhail Zhitlukhin: Steklov Mathematical Institute of the Russian Academy of Sciences

Annals of Finance, 2020, vol. 16, issue 4, No 3, 529-546

Abstract: Abstract We consider a game-theoretic model of a market where investors compete for payoffs yielded by several assets. The main result consists in a proof of the existence and uniqueness of a strategy, called relative growth optimal, such that the logarithm of the share of its wealth in the total wealth of the market is a submartingale for any strategies of the other investors. It is also shown that this strategy is asymptotically optimal in the sense that it achieves the maximal capital growth rate when compared to competing strategies. Based on the results obtained, we study the asymptotic structure of the market when all the investors use the relative growth optimal strategy.

Keywords: Relative growth optimal strategy; Asset market game; Evolutionary finance; Martingale convergence (search for similar items in EconPapers)
JEL-codes: C73 G11 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:kap:annfin:v:16:y:2020:i:4:d:10.1007_s10436-020-00360-6

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DOI: 10.1007/s10436-020-00360-6

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