# Doubly reflected BSDEs with call protection and their approximation

Jean-François Chassagneux; Stéphane Crépey

ESAIM: Probability and Statistics (2014)

- Volume: 18, page 613-641
- ISSN: 1292-8100

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topChassagneux, Jean-François, and Crépey, Stéphane. "Doubly reflected BSDEs with call protection and their approximation." ESAIM: Probability and Statistics 18 (2014): 613-641. <http://eudml.org/doc/274342>.

@article{Chassagneux2014,

abstract = {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.},

author = {Chassagneux, Jean-François, Crépey, Stéphane},

journal = {ESAIM: Probability and Statistics},

keywords = {reflected BSDEs; variational inequalities; discrete-time approximation; game option; Call protection; reflected backward stochastic differential equations (BSDEs); call protection},

language = {eng},

pages = {613-641},

publisher = {EDP-Sciences},

title = {Doubly reflected BSDEs with call protection and their approximation},

url = {http://eudml.org/doc/274342},

volume = {18},

year = {2014},

}

TY - JOUR

AU - Chassagneux, Jean-François

AU - Crépey, Stéphane

TI - Doubly reflected BSDEs with call protection and their approximation

JO - ESAIM: Probability and Statistics

PY - 2014

PB - EDP-Sciences

VL - 18

SP - 613

EP - 641

AB - 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.

LA - eng

KW - reflected BSDEs; variational inequalities; discrete-time approximation; game option; Call protection; reflected backward stochastic differential equations (BSDEs); call protection

UR - http://eudml.org/doc/274342

ER -

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