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

by Mikhail Zhitlukhin1
1Steklov Mathematical Institute of the Russian Academy of Sciences. 8 Gubkina St., Moscow, Russia
(email: mikhailzh@mi-ras.ru)


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 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.

Key words:

Asset market game, Relative growth optimal strategy, Martingale convergence, Evolutionary finance
JEL Classification:  C73, G11
Mathematics Subject Classification (2020): 91A25, 91B55