European and american options in a non-linear incomplete market with default | Vidéo | Carmin.tv

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European and american options in a non-linear incomplete market with default

By Marie-Claire Quenez

Appears in collection : Advances in Stochastic Control and Optimal Stopping with Applications in Economics and Finance / Avancées en contrôle stochastique et arrêt optimal avec applications à l'économie et à la finance

We study the superhedging prices and the associated superhedging strategies for European options in a nonlinear incomplete market model with default. The underlying market model consists of one risk-free asset and one risky asset, whose price may admit a jump at the default time. The portfolio processes follow nonlinear dynamics with a nonlinear driver $f$. By using a dynamic programming approach, we first provide a dual formulation of the seller's (superhedging) price for the European option as the supremum, over a suitable set of equivalent probability measures $Q \in \mathcal{Q}$, of the $f$ - evaluation/expectation under $Q$ of the payoff. We also establish a characterization of the seller's (superhedging) price as the initial value of the minimal supersolution of a constrained backward stochastic differential equation with default. Moreover, we provide some properties of the terminal profit made by the seller, and some results related to replication and no-arbitrage issues. Our results rely on first establishing a nonlinear optional and a nonlinear predictable decomposition for processes which are $\mathcal{E}^f$-strong supermartingales under $Q$ for all $Q \in \mathcal{Q}$. Joint work with M. Grigorova and A. Sulem.

Information about the video

Date of recording 13/09/2022
Date of publication 27/09/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19959703
Cite this video Quenez, Marie-Claire (13/09/2022). European and american options in a non-linear incomplete market with default. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19959703
URL https://dx.doi.org/10.24350/CIRM.V.19959703

Domain(s)

Probability

Bibliography

GRIGOROVA, Miryana, QUENEZ, Marie-Claire, et SULEM, Agnès. European Options in a Nonlinear Incomplete Market Model with Default. SIAM Journal on Financial Mathematics, 2020, vol. 11, no 3, p. 849-880. - https://doi.org/10.1137/20M1318018

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