The Minimum Maximum of a Continuous Martingale with given Initial and Terminal Laws By
نویسندگان
چکیده
Let (Mt )0≤t≤1 be a continuous martingale with initial law M0 ∼ μ0, and terminal law M1 ∼ μ1, and let S = sup0≤t≤1Mt . In this paper we prove that there exists a greatest lower bound with respect to stochastic ordering of probability measures, on the law of S. We give an explicit construction of this bound. Furthermore a martingale is constructed which attains this minimum by solving a Skorokhod embedding problem. The form of this martingale is motivated by a simple picture. The result is applied to the robust hedging of a forward start digital option.
منابع مشابه
The Minimum Maximum of a Continuous Martingale with Given Initial and Terminal Laws
Let (Mt)0≤t≤1 be a continuous martingale with initial lawM0 ∼ μ0, and terminal lawM1 ∼ μ1, and let S = sup 0≤t≤1 Mt. In this paper we prove that there exists a greatest lower bound with respect to stochastic ordering of probability measures, on the law of S. We give an explicit construction of this bound. Furthermore a martingale is constructed which attains this minimum by solving a Skorokhod ...
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