evenements:seminaireproba-math-fi
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evenements:seminaireproba-math-fi [2019/12/16 21:50] Valérie Picot |
evenements:seminaireproba-math-fi [2019/12/16 21:50] Valérie Picot |
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| **__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// | + | **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. | ++ 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. | 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. | ||
evenements/seminaireproba-math-fi.txt · Last modified: 2024/05/21 07:28 by Valérie Picot
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