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.
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.
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@article{CRMATH_2018__356_4_433_0, author = {Gu\'eant, Olivier}, title = {Expected {Shortfall} and optimal hedging payoff}, journal = {Comptes Rendus. Math\'ematique}, pages = {433--438}, publisher = {Elsevier}, volume = {356}, number = {4}, year = {2018}, doi = {10.1016/j.crma.2018.03.010}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2018.03.010/} }
TY - JOUR AU - Guéant, Olivier TI - Expected Shortfall and optimal hedging payoff JO - Comptes Rendus. Mathématique PY - 2018 SP - 433 EP - 438 VL - 356 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.03.010/ DO - 10.1016/j.crma.2018.03.010 LA - en ID - CRMATH_2018__356_4_433_0 ER -
Guéant, Olivier. Expected Shortfall and optimal hedging payoff. Comptes Rendus. Mathématique, Tome 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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