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Abstract
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When the discounted stock price is a martingale under the risk neutral measure, it is well know that exercising the American call option at the terminal time is optimal. However, it may not be the case when the discounted stock price is a strict local martingale. In this talk, I will present how to price and optimally exercise American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical Analysis, 15:89-168, 2009]. The relationship between the martingale property of diffusion processes and the uniqueness of classical solutions for Cauchy problems will be also discussed. |
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