In this work, we analyze a nonlinear partial differential equation (PDE) model for the total value adjustment on European options in the presence of a counterparty risk. We transform the nonlinear PDE into an equivalent one, involving a sectorial operator, and prove the existence and uniqueness of a solution.
Dans ce travail, nous analysons un modèle d'équations aux dérivées partielles (EDP) non linéaires pour l'ajustement XVA d'options européennes en présence d'un risque de contrepartie. Nous transformons l'EDP non linéaire en une équation équivalente, impliquant un opérateur sectoriel, et prouvons l'existence et l'unicité de la solution.
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@article{CRMATH_2019__357_3_252_0, author = {Arregui, I\~nigo and Salvador, Beatriz and \v{S}ev\v{c}ovi\v{c}, Daniel and V\'azquez, Carlos}, title = {Mathematical analysis of a nonlinear {PDE} model for {European} options with counterparty risk}, journal = {Comptes Rendus. Math\'ematique}, pages = {252--257}, publisher = {Elsevier}, volume = {357}, number = {3}, year = {2019}, doi = {10.1016/j.crma.2019.03.001}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2019.03.001/} }
TY - JOUR AU - Arregui, Iñigo AU - Salvador, Beatriz AU - Ševčovič, Daniel AU - Vázquez, Carlos TI - Mathematical analysis of a nonlinear PDE model for European options with counterparty risk JO - Comptes Rendus. Mathématique PY - 2019 SP - 252 EP - 257 VL - 357 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2019.03.001/ DO - 10.1016/j.crma.2019.03.001 LA - en ID - CRMATH_2019__357_3_252_0 ER -
%0 Journal Article %A Arregui, Iñigo %A Salvador, Beatriz %A Ševčovič, Daniel %A Vázquez, Carlos %T Mathematical analysis of a nonlinear PDE model for European options with counterparty risk %J Comptes Rendus. Mathématique %D 2019 %P 252-257 %V 357 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2019.03.001/ %R 10.1016/j.crma.2019.03.001 %G en %F CRMATH_2019__357_3_252_0
Arregui, Iñigo; Salvador, Beatriz; Ševčovič, Daniel; Vázquez, Carlos. Mathematical analysis of a nonlinear PDE model for European options with counterparty risk. Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 252-257. doi : 10.1016/j.crma.2019.03.001. http://archive.numdam.org/articles/10.1016/j.crma.2019.03.001/
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