A continuous-time asset market game with short-lived assets

We propose a continuous-time game-theoretic model of an investment market with short-lived assets. The first goal of the paper is to obtain a stochastic equation which determines the wealth processes of investors and to provide conditions for the existence of its solution. The second goal is to show...

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Bibliographic Details
Published in:Finance and stochastics 2022-07, Vol.26 (3), p.587-630
Main Author: Zhitlukhin, Mikhail
Format: Article
Language:English
Subjects:
Assets
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Game theory
Insurance
Management
Mathematics
Mathematics and Statistics
Payoffs
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Strategy
Wealth
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Summary:We propose a continuous-time game-theoretic model of an investment market with short-lived assets. The first goal of the paper is to obtain a stochastic equation which determines the wealth processes of investors and to provide conditions for the existence of its solution. The second goal is to show that there exists a strategy such that the logarithm of the relative wealth of an investor who uses it is a submartingale regardless of the strategies of the other investors, and the relative wealth of any other essentially different strategy vanishes asymptotically. This strategy can be considered as an optimal growth portfolio in the model.
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-022-00479-6