Processes of class Sigma, last passage times, and drawdowns

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dc.contributor.author Cheridito, Patrick en_US
dc.contributor.author Nikeghbali, Ashkan en_US
dc.contributor.author Platen, Eckhard en_US
dc.contributor.editor en_US
dc.date.accessioned 2012-10-12T03:32:50Z
dc.date.available 2012-10-12T03:32:50Z
dc.date.issued 2012 en_US
dc.identifier 2011003681 en_US
dc.identifier.citation Cheridito Patrick, Nikeghbali Ashkan, and Platen Eckhard 2012, 'Processes of class Sigma, last passage times, and drawdowns', Society for Industrial and Applied Mathematics, vol. 3, pp. 280-303. en_US
dc.identifier.issn 1945-497X en_US
dc.identifier.other C1 en_US
dc.identifier.uri http://hdl.handle.net/10453/17960
dc.description.abstract We propose a general framework for studying last passage times, suprema, and drawdowns of a large class of continuous-time stochastic processes. Our approach is based on processes of class Sigma and the more general concept of two processes, one of which moves only when the other is at the origin. After investigating certain transformations of such processes and their convergence properties, we provide three general representation results. The first allows the recovery of a process of class Sigma from its final value and the last time it visited the origin. In many situations this gives access to the distribution of the last time a stochastic process attains a certain level or is equal to its running maximum. It also leads to recently discovered formulas expressing option prices in terms of last passage times. Our second representation result is a stochastic integral representation that will allow us to price and hedge options on the running maximum of an underlying that are triggered when the underlying drops to a given level or, alternatively, when the drawdown or relative drawdown of the underlying attains a given height. The third representation gives conditional expectations of certain functionals of processes of class Sigma. It can be used to deduce the distributions of a variety of interesting random variables such as running maxima, drawdowns, and maximum drawdowns of suitably stopped processes. en_US
dc.language en_US
dc.publisher Society for Industrial and Applied Mathematics en_US
dc.relation.isbasedon http://dx.doi.org/10.1137/09077878X en_US
dc.title Processes of class Sigma, last passage times, and drawdowns en_US
dc.parent SIAM Journal on Financial Mathematics en_US
dc.journal.volume 3 en_US
dc.journal.number en_US
dc.publocation US en_US
dc.identifier.startpage 280 en_US
dc.identifier.endpage 303 en_US
dc.cauo.name SCI.Mathematical Sciences en_US
dc.conference Verified OK en_US
dc.for 010200 en_US
dc.personcode 0000076250 en_US
dc.personcode 0000050470 en_US
dc.personcode 970685 en_US
dc.percentage 100 en_US
dc.classification.name Applied Mathematics en_US
dc.classification.type FOR-08 en_US
dc.edition en_US
dc.custom en_US
dc.date.activity en_US
dc.location.activity en_US
dc.description.keywords processes of class Sigma; last passage times; drawdowns; relative drawdowns; maximum drawdowns; options on running maxima en_US
dc.staffid en_US
dc.staffid 970685 en_US


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