Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty
MathematicS In Action, Volume 11 (2022) no. 1, pp. 193-212.

We solve the problem of super-hedging European or Asian options for discrete-time financial market models where executable 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 numerical procedure to compute the infimum price 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 the super-hedging problem. We illustrate our method by a numerical example.

Published online:
DOI: 10.5802/msia.24
Classification: 49J53,  60D05,  91G80
Keywords: Super-hedging prices, Delayed information, Uncertainty, Conditional random sets, AIP Condition
Meriam El Mansour 1; Emmanuel Lépinette 1

1 CEREMADE, UMR CNRS 7534, Paris Dauphine University, PSL National Research, Place du Maréchal De Lattre De Tassigny, 75775 Paris cedex 16, France, and Gosaef, Faculty of Sciences of Tunis, Tunisia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Meriam El Mansour; Emmanuel Lépinette. Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty. MathematicS In Action, Volume 11 (2022) no. 1, pp. 193-212. doi : 10.5802/msia.24. https://msia.centre-mersenne.org/articles/10.5802/msia.24/

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