Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance

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dc.creatorKaroui, Nicole El
dc.creatorMeziou, Asma
dc.date2008-04-16
dc.date.accessioned2026-07-07T12:18:21Z
dc.date.available2026-07-07T12:18:21Z
dc.descriptionWe are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows, in particular, to solve the American optimal stopping problem without having to compute the option price. Some illustrative examples based on one-dimensional diffusion processes are then provided. Another interesting application concerns the portfolio insurance. Hence, based on the ``Max-Plus martingale,'' we solve in the paper an optimization problem whose aim is to find the best martingale dominating a given floor process (on every intermediate date), w.r.t. the convex order on terminal values.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009117907000000222 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0804.2561
dc.identifierhttp://arxiv.org/abs/0804.2561
dc.identifierAnnals of Probability 2008, Vol. 36, No. 2, 647-697
dc.identifierdoi:10.1214/009117907000000222
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212380
dc.subjectPricing of Securities
dc.subjectProbability
dc.subject60G07, 60G40, 60G51, 16Y60, 60E15 (Primary) 91B28, 60G44 (Secondary)
dc.titleMax-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance
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