TY - THES
T1 - Discretization of backward stochastic Volterra integral equations
A1 - Pokalyuk,Stanislav
Y1 - 2012/06/28
N2 - We generalize a numerical method for backward stochastic differential equations by Ma et al. (Ann. Appl. Probab. 12, 2002) to backward stochastic Volterra integral equations (BSVIEs, for short). Under certain regularity conditions on the coefficients the adapted M-solution of the BSVIE can be approximated by a sequence of discrete BSVIEs (DBSVIEs, for short) driven by a binary random walk. Precisely, we show that the sequence of discrete solutions from the obtained DBSVIE converges weakly to the continuous solution from the BSVIE in the Skorokhod topology. As a main tool for the proof we relate the M-solution of our BSVIE to a non-standard system of quasilinear partial differential equation of parabolic type. We finally illustrate the convergence result by a numerical example.
KW - Numerisches Verfahren
KW - Volterra-Integralgleichung
KW - Stochastik
CY - Saarbrücken
PB - Saarländische Universitäts- und Landesbibliothek
AD - Postfach 151141, 66041 Saarbrücken
UR - http://scidok.sulb.uni-saarland.de/volltexte/2012/4882
ER -