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Comptes Rendus Mathématique
Volume 354, n° 11
pages 1101-1108 (novembre 2016)
Doi : 10.1016/j.crma.2016.09.015
Received : 25 Mars 2016 ;  accepted : 26 September 2016
An existence theorem for multidimensional BSDEs with mixed reflections
Un théorème d'existence pour les EDSRs multidimensionnelles avec réflexions mixtes
 

Yuhong Xu
 Mathematical Center for Interdiscipline Research and School of Mathematical Sciences, Soochow University, Suzhou 215006, PR China 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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.

The full text of this article is available in PDF format.

 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.

1  The French abbreviation for right continuous and left limited, or RCLL for short.


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