Relative growth optimal strategies in an asset market game

IF 0.8 Q4 BUSINESS, FINANCE

Annals of Finance Pub Date : 2020-03-02 DOI:10.1007/s10436-020-00360-6

Yaroslav Drokin, Mikhail Zhitlukhin

引用次数: 5

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.

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资产市场博弈中的相对增长最优策略

我们考虑了一个市场的博弈论模型，在这个模型中，投资者争夺几种资产的收益。主要结果在于证明了一种称为相对增长最优的策略的存在性和唯一性，使得其财富在市场总财富中所占份额的对数是其他投资者任何策略的子映射。研究还表明，与竞争策略相比，该策略在实现最大资本增长率的意义上是渐近最优的。基于所得结果，我们研究了当所有投资者都使用相对增长最优策略时市场的渐近结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Finance BUSINESS, FINANCE-

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Finance provides an outlet for original research in all areas of finance and its applications to other disciplines having a clear and substantive link to the general theme of finance. In particular, innovative research papers of moderate length of the highest quality in all scientific areas that are motivated by the analysis of financial problems will be considered. Annals of Finance''s scope encompasses - but is not limited to - the following areas: accounting and finance, asset pricing, banking and finance, capital markets and finance, computational finance, corporate finance, derivatives, dynamical and chaotic systems in finance, economics and finance, empirical finance, experimental finance, finance and the theory of the firm, financial econometrics, financial institutions, mathematical finance, money and finance, portfolio analysis, regulation, stochastic analysis and finance, stock market analysis, systemic risk and financial stability. Annals of Finance also publishes special issues on any topic in finance and its applications of current interest. A small section, entitled finance notes, will be devoted solely to publishing short articles – up to ten pages in length, of substantial interest in finance. Officially cited as: Ann Finance