  We consider a continuous-time game-theoretic model of an investment market
with short-lived assets and endogenous asset prices. The first goal of the
paper is to formulate 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.
