Prof. Dr. Martin Hutzenthaler (Goethe-Universität Frankfurt):
Limitations of the Euler method
Time and place
Thursday, 24.1.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Abstract
Our goal is to calculate moments of stochastic differential equations (SDEs)\n(e.g. the stochastic Langevin equation, the stochastic Duffing-van der Pol\nequation, the stochastic Lotka-Volterra model, the Lewis-3/2-volatility\nmodel, the stochastic Lorenz equation). In the global Lipschitz case, the\napproximation method with optimal rate of convergence is the multilevel\nMonte Carlo Euler method. Most of the applied SDEs, however, have\nsuper-linearly growing coefficients. We show for this case that the\nmultilevel Monte Carlo Euler method does not even converge in general. The\nreason herefore is strong divergence of Euler's method. For this reason, we\nrecommend to be careful with Euler's method in applications. Instead, we\npropose a strongly converging numerical method with optimal rate of\nconvergence and provide its short Matlab code.\n