Probability theory/Calculus of variations
Expected Shortfall and optimal hedging payoff
Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 433-438.

By using variational techniques, we provide an optimal payoff written on a given random variable for hedging – in the sense of minimizing the Expected Shortfall at a given threshold – a payoff written on another random variable. In numerous financially relevant examples, our result leads to optimal payoffs in closed form. From a theoretical viewpoint, our result is also useful for providing bounds to the classical Expected Shortfall minimization problem with given financial instruments.

En utilisant des techniques de calcul variationnel, nous obtenons un payoff, fonction d'une variable aléatoire fixée, permettant de couvrir optimalement – au sens de la minimisation de l'Expected Shortfall à un seuil donné – un payoff fonction d'une autre variable aléatoire. Dans de nombreux cas pertinents en finance, le résultat obtenu aboutit à des payoffs optimaux en formule fermée. Du point de vue théorique, le résultat obtenu fournit aussi des bornes pour le problème classique de la minimisation de l'Expected Shortfall avec des instruments financiers donnés.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.03.010
Guéant, Olivier 1

1 CES – Université Paris-1, Panthéon-Sorbonne, 106, boulevard de l'Hôpital, 75013 Paris, France
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Guéant, Olivier. Expected Shortfall and optimal hedging payoff. Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 433-438. doi : 10.1016/j.crma.2018.03.010. http://www.numdam.org/articles/10.1016/j.crma.2018.03.010/

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