Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty
El Mansour, Meriam; Lépinette, Emmanuel (2021), Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty. https://basepub.dauphine.psl.eu/handle/123456789/22852
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-03161157
Series titleCahier de recherche CEREMADE, Université Paris Dauphine-PSL
MetadataShow full item record
Author(s)El Mansour, Meriam
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We solve the problem of super-hedging European or Asian options for discrete-time financial market models where executed prices are uncertain. The risky asset prices are not described by single-valued processes but measurable selections of random sets that allows to consider a large variety of models including bid-ask models with order books, but also models with a delay in the execution of the orders. We provide a dynamic programming principle under a weak no-arbitrage condition, the so-called AIP condition, under which the prices of the non negative European options are non negative. This condition is weaker than the existence of a risk-neutral martingale measure but it is sufficient to numerically solve completely the super-hedging problem. We illustrate our method by a numerical example.
Subjects / KeywordsSuper-hedging prices; Delayed information; Uncertainty; Conditional random sets; AIP condition; Robust Finance
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