Abstract
We develop a class of pathwise inequalities of the form H(Bt)≥Mt+F(Lt), where Bt is Brownian motion, Lt its local time at zero and Mt a local martingale. The concrete nature of the representation makes the inequality useful for a variety of applications. In this work, we use the inequalities to derive constructions and optimality results of Vallois’ Skorokhod embeddings. We discuss their financial interpretation in the context of robust pricing and hedging of options written on the local time. In the final part of the paper we use the inequalities to solve a class of optimal stopping problems of the form
Citation
A. M. G. Cox. David Hobson. Jan Obłój. "Pathwise inequalities for local time: Applications to Skorokhod embeddings and optimal stopping." Ann. Appl. Probab. 18 (5) 1870 - 1896, October 2008. https://doi.org/10.1214/07-AAP507
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