evenements:seminaireproba-math-fi
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
|
evenements:seminaireproba-math-fi [2019/11/25 13:46] Valérie Picot |
evenements:seminaireproba-math-fi [2019/12/16 21:50] Valérie Picot |
||
|---|---|---|---|
| Line 7: | Line 7: | ||
| **__Exposés de l'année 2019__ :** | **__Exposés de l'année 2019__ :** | ||
| + | |||
| + | **jeudi 19 décembre à 15h00 :** <color #088A85> Miryana Grigorova</color>(University of Leeds) //A non-linear incomplete market model with default: Pricing of European and American options// | ||
| + | ++ Voir résumé | \\ We present an incomplete market model with default which consists of one risky asset with dynamics driven by two "sources of risk", namely a Brownian motion and a compensated default martingale. Additionally to this feature, the wealth process follows non-linear dynamics with a non-linear driver f, which allows to incorporate a number of imperfections in the market. | ||
| + | We thus face a non-linear incomplete market with default. We provide a dual formulation of the seller's superhedging price for a European option in terms of the supremum, over a suitable set of equivalent probability measures Q, of the non-linear f-evaluation/expectation under Q of the payoff. We also provide some related criteria for replicability of a given pay-off. By a form of symmetry, we derive corresponding results for the buyer. Our results rely on first establishing a non-linear optional decomposition for processes which are (non-linear) f-strong supermartingales under Q, for all Q. This decomposition is the analogue in our framework of the well-known optional decomposition from the linear case. We also show that the non-linear optional decomposition is equivalent to a non-linear predictable decomposition with constraints. | ||
| + | This result allows us to show an infinitesimal characterization of the seller's (superhedging) price process as the minimal supersolution of a constrained BSDE with default. | ||
| + | We will also discuss corresponding results for the seller's superhedging price of an American option. | ||
| + | |||
| + | The talk is based on joint works with Marie-Claire Quenez and Agnès Sulem. | ||
| + | ++ | ||
| **28 novembre à 14h00 :** <color #088A85> Marie-Amélie Morlais </color>(Université du Mans) // Problème de commutation optimale avec nombre infini de modes : Une approche par “randomisation” et caractérisation par une EDSR avec contraintes sur les sauts// | **28 novembre à 14h00 :** <color #088A85> Marie-Amélie Morlais </color>(Université du Mans) // Problème de commutation optimale avec nombre infini de modes : Une approche par “randomisation” et caractérisation par une EDSR avec contraintes sur les sauts// | ||
evenements/seminaireproba-math-fi.txt · Last modified: 2024/04/22 12:08 by Valérie Picot
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 3.0 Unported
