Relative growth optimal strategies in an asset market game
Mathematical Finance
2020-07-24 v2
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
Cite
@article{arxiv.1908.01171,
title = {Relative growth optimal strategies in an asset market game},
author = {Yaroslav Drokin and Mikhail Zhitlukhin},
journal= {arXiv preprint arXiv:1908.01171},
year = {2020}
}
Comments
16 pages. Published in "Annals of Finance"