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An Optimization Approach to Weak Approximation of Lévy-Driven Stochastic Differential Equations
chapterposted on 2010-06-22, 13:36 authored by Kenji Kashima, Reiichiro Kawai
We propose an optimization approach to weak approximation of Lévy-driven stochastic differential equations. We employ a mathematical programming framework to obtain numerically upper and lower bound estimates of the target expectation, where the optimization procedure ends up with a polynomial programming problem. An advantage of our approach is that all we need is a closed form of the Lévy measure, not the exact simulation knowledge of the increments or of a shot noise representation for the time discretization approximation. We also investigate methods for approximation at some different intermediate time points simultaneously.