In this paper we show that a Kelly trader is indifferent to trade a derivative if and only if the no-arbitrage price is uniquely given by the minimal martingale measure 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.

中文翻译：

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凯利交易和期权定价

在本文中，我们表明当且仅当无套利价格由最小鞅度量价格唯一给出时，凯利交易者对交易衍生品无动于衷，从而为不完全市场中的期权定价提供了自然选择机制。我们还表明，独特的凯利无差异价格导致市场均衡，因为考虑到其他市场参与者的行为，没有凯利交易者可以通过交易衍生品来提高其瞬时夏普比率的幅度。