TY  - THES
T1  - Numerical solutions of BSDEs : a-posteriori estimates and enhanced least-squares Monte Carlo
A1  - Steiner,Jessica
Y1  - 2012/12/04
N2  - Backward stochastic differential equations (BSDEs) are a powerful tool in financial mathematics. Important examples are option pricing or portfolio selection problems. In non-linear cases BSDEs are usually not solvable in closed form and approximation becomes then inevitable. Several proposals for solving BSDEs numerically have been published in recent years, including an analysis of the related approximation error. The first part of this theses is devoted to the problem that a direct a-posteriori evaluation of the L^2-error between the true solution and some numerical solution is usually impossible. Therefore, we present an a-posteriori criterion on the approximation error, which is computable in terms of the numerical solution only and allows us to judge the numerical solution. Secondly, we pick up the idea of Gobet, Lemor and Warin (Ann. Appl. Probab., 15, 2172 - 2202 (2005)) to generate numerical solutions by least-squares Monte Carlo. We suggest to use function bases that form a system of martingales. A complete analysis of the approximation error shows, that in contrast to original least-squares Monte Carlo, the convergence behaviour can be significantly enhanced by the martingale property of the bases.
KW  - Monte-Carlo-Simulation
KW  - Numerische Mathematik
KW  - Stochastische Differentialgleichung
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4971
ER  -