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Pathwise inequalities for local time: applications to Skorokhod embeddings and optimal stopping


Reference:

Cox, A. M. G., Hobson, D. and Obloj, J., 2008. Pathwise inequalities for local time: applications to Skorokhod embeddings and optimal stopping. Annals of Applied Probability, 18 (5), pp. 1870-1896.

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http://projecteuclid.org/euclid.aoap/1225372954

Abstract

We develop a class of pathwise inequalities of the form H(B-t) >= M-t + F(L-t), where B-t is Brownian motion, L-t its local time at zero and M-t 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 sup(tau) E[F(L-tau) - integral(t)(0) beta(B-s)ds]. The solution is given via a minimal solution to a system of differential equations and thus resembles the maximality principle described by Peskir. Throughout, the emphasis is placed on the novelty and simplicity of the techniques.

Details

Item Type Articles
CreatorsCox, A. M. G., Hobson, D. and Obloj, J.
DOI10.1214/07-AAP507
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code12084
Additional InformationID number: 000260850800010

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