Kelly trading and option pricing

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Abstract

In this paper we show that a Kelly trader is indifferent to trade the derivative if and only if the no-arbitrage price is uniquely given by the minimal martingale measure no-arbitrage price, thus providing a natural selection mechanism for option pricing in incomplete markets. We also show that the unique Kelly indifference price results in market equilibrium, in the sense that no Kelly trader can improve the magnitude of his instantaneous Sharpe ratio, by trading the derivative, given the actions of the other market participants.