

Principle Seminar of the Department of Probability Theory, Moscow State University
October 31, 2018 16:45–17:45, Moscow, MSU, auditorium 1224






Asymptotic distribution of capital in a market model with competition
M. V. Zhitlukhin^{} ^{} Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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Abstract:
We consider a stochastic gametheoretic model of an investment market
with continuous time, where investors compete for the distribution of
income from several assets. The main results are related to the question
in what proportions the total capital will be distributed among the
investors, and what will be the prices of the assets asymptotically on
the infinite time horizon depending on the strategies of the investors.
We prove that there exists a strategy with the following properties:
1) the proportion of its capital on the entire time horizon is separated
from zero with probability 1 regardless of the strategies of
competitors;
2) the relative asset prices are asymptotically determined
by it;
3) the proportion of capital of investors who follow essentially
different strategies tends to zero.
This strategy is analogous to the
Kelly (growthoptimal) strategy in stock market models without competition.

