An optimal stopping approach to the n-marginal Root problem

Alexander Cox (University of Bath)

Frank Adams 2,

Recently, financial applications have generated renewed interest in solutions to the classical Skorokhod Embedding Problem (SEP), as well as some natural generalisations. Of particular interest are solutions which demonstrate optimality properties within the class of solutions to the SEP. In this talk, we consider a generalisation of Root's solution to the SEP where we look for an ordered sequence of stopping times, each of which embeds a given distribution. We are able to identify these stopping times as the exit times from certain domains, and we are able to characterise these domains naturally as the stopping regions of a suitable multiple stopping problem. Moreover, we are able to show optimality for these stopping times by solving an associated dual problem. (Joint work with Jan Obloj and Nizar Touzi.)

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