[Un théorème d'existence pour les EDSRs multidimensionnelles avec réflexions mixtes]
Dans cette note, on considère le problème du pricing pour un certain type d'option réelle, donnant les droits de changer le mode d'investissement et d'abandonner le projet d'investissement avant son échéance. La valeur de cette option peut être caractérisée par les solutions des équations différentielles stochastiques rétrogrades (EDSRs) avec deux types de réflexions aux bords, normale et oblique, dont les coefficients sont à croissance linéaire et sont lipschitziens en y à gauche ainsi que lipschitziens en z. Dans ce cadre, on fournit un théorème d'existence des solutions minimales pour les EDSRs.
In this note, we consider the pricing problem for a type of real option, which gives the right to switch investment modes and abandon the investment project before its maturity. The value of this option can be characterized by solutions to multidimensional backward stochastic differential equations (BSDEs) with both normal and oblique reflections, whose coefficients are of linear growth and are left-Lipschitz with respect to (w.r.t) y and Lipschitz w.r.t. z. We provide an existence theorem of minimal solutions for BSDEs in this framework.
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@article{CRMATH_2016__354_11_1101_0,
author = {Xu, Yuhong},
title = {An existence theorem for multidimensional {BSDEs} with mixed reflections},
journal = {Comptes Rendus. Math\'ematique},
pages = {1101--1108},
publisher = {Elsevier},
volume = {354},
number = {11},
year = {2016},
doi = {10.1016/j.crma.2016.09.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.09.015/}
}
TY - JOUR AU - Xu, Yuhong TI - An existence theorem for multidimensional BSDEs with mixed reflections JO - Comptes Rendus. Mathématique PY - 2016 SP - 1101 EP - 1108 VL - 354 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.09.015/ DO - 10.1016/j.crma.2016.09.015 LA - en ID - CRMATH_2016__354_11_1101_0 ER -
%0 Journal Article %A Xu, Yuhong %T An existence theorem for multidimensional BSDEs with mixed reflections %J Comptes Rendus. Mathématique %D 2016 %P 1101-1108 %V 354 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.09.015/ %R 10.1016/j.crma.2016.09.015 %G en %F CRMATH_2016__354_11_1101_0
Xu, Yuhong. An existence theorem for multidimensional BSDEs with mixed reflections. Comptes Rendus. Mathématique, Tome 354 (2016) no. 11, pp. 1101-1108. doi : 10.1016/j.crma.2016.09.015. http://www.numdam.org/articles/10.1016/j.crma.2016.09.015/
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Cité par Sources :
☆ The work is partially supported by the Natural Science Foundation of China (No. 11401414) and of Jiangsu province (No. BK20140299; No. 14KJB110022) and PAPD and the collaborative innovation center for quantitative calculation and control of financial risk.
