A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations

We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the timestep h higher than O(√h). We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to ℝ48. The paper is self-contained and the code will be made freely downloadable.

weak convergence; feynman-kac; stochastic differential equation; bounded difusión; first-exit problem

A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations Articles