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We consider a stochastic game-theoretic model of a discrete-time asset marketwith short-lived assets and endogenous asset prices. We prove that the strategywhich invests in the assets proportionally to their expected relative payoffsasymptotically minimizes the expected time needed to reach a large wealthlevel. The result is obtained under the assumption that the relative assetpayoffs and the growth rate of the total payoff during each time period areindependent and identically distributed.

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