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An optimal stopping approach to the n-marginal Root problem, and applications to variance options

Banff International Research Station for Mathematical Innovation and Discovery

Recently, the problem of finding robust bounds on option\r\nprices which incorporate information from vanilla options has generated\r\nrenewed interest in solutions to the classical Skorokhod Embedding\r\nProblem (SEP). It is natural to consider generalisations of the problem\r\nwhere the prices of the vanilla options are known both at the maturity\r\nof the option, and also at intermediate times. In this talk, we consider\r\na generalisation of Root\'s solution to the SEP where we look for an\r\nordered sequence of stopping times, each of which embeds a given\r\ndistribution. In particular, we are able to identify these stopping\r\ntimes as the exit times from certain domains, and we are able to\r\ncharacterise these domains naturally as the stopping regions of a\r\nsuitable multiple stopping problem. Moreover, we are able to show\r\noptimality for these stopping times, and hence derive sub-hedging\r\nstrategies which enforce the price bounds in any suitable model. \r\n\r\n(Joint work with Jan Obloj and Nizar Touzi)

Mathematics; Game theory, economics, social and behavioral sciences; Probability theory and stochastic processes; Mathematical finance

video/mp4

Author affiliation: University of Bath

2014-10-30

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50936

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/