Volume 18, 2014
|Page(s)||613 - 641|
|Published online||15 October 2014|
Doubly reflected BSDEs with call protection and their approximation
Revised: 24 January 2013
We study the numerical approximation of doubly reflected backward stochastic differential equations with intermittent upper barrier (RIBSDEs). These denote reflected BSDEs in which the upper barrier is only active on certain random time intervals. From the point of view of financial interpretation, RIBSDEs arise as pricing equations of game options with constrained callability. In a Markovian set-up we prove a convergence rate for a time-discretization scheme by simulation to an RIBSDE. We also characterize the solution of an RIBSDE as the largest viscosity subsolution of a related system of variational inequalities, and we establish the convergence of a deterministic numerical scheme for that problem. Due to the potentially very high dimension of the system of variational inequalities, this approach is not always practical. We thus subsequently prove a convergence rate for a time-discretisation scheme by simulation to an RIBSDE.
Mathematics Subject Classification: 93E20 / 65C99 / 60H30
Key words: Reflected BSDEs / Variational inequalities / Discrete-time approximation / Game option / Call protection
This research benefited from the support of the “Chair Markets in Transition” under the aegis of Louis Bachelier laboratory, a joint initiative of École polytechnique, Université d’Évry Val d’Essonne and Fédération Bancaire Française. The paper was completed during a visit to the Hausdorff Research Institute for Mathematics at the University of Bonn in the framework of the Trimester Program Stochastic Dynamics in Economics and Finance.
© EDP Sciences, SMAI, 2014
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