Asymptotic minimization of expected time to reach a large wealth level in an asset market game

A stochastic game-theoretic model of a discrete-time asset market with short-lived assets and endogenous asset prices is considered. It is proved that the strategy which invests in the assets proportionally to their expected relative payoffs asymptotically minimizes the expected time needed to reach a large wealth level under the assumption that the total payoffs of the assets are i.i.d. and the relative payoffs are bounded away from zero.