Robust discrete-time super-hedging strategies under AIP condition and under price uncertainty
Meriam El Mansour1; Emmanuel Lépinette1
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
MathematicS In Action, Special issue Maths and Industry, 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
Mots-clés : 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, Special issue Maths and Industry, 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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