论文标题
用于抛物线抛物线差异方程的Dirichlet问题的随机步行算法
Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation
论文作者
论文摘要
我们考虑由一般lévy过程（SDE）驱动的随机微分方程，具有无限活性，以及通过Feynman-kac公式的相关性，抛物线抛物性透明度分化方程（PIDE）的差异问题。我们使用SDE的数值方法近似Pide的解。该方法基于三种成分：（i）我们通过扩散近似小跳跃； （ii）我们使用受限制的跳跃自适应时间步变； （iii）在跳跃之间，我们利用了弱的Euler近似。我们证明了所考虑算法的弱收敛性，并对其误差和计算成本如何取决于跳跃活动水平进行了深入的分析。提出了一些数值实验的结果，包括屏障篮子货币期权的定价。
We consider stochastic differential equations driven by a general Lévy processes (SDEs) with infinite activity and the related, via the Feynman-Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). We approximate the solution of PIDE using a numerical method for the SDEs. The method is based on three ingredients: (i) we approximate small jumps by a diffusion; (ii) we use restricted jump-adaptive time-stepping; and (iii) between the jumps we exploit a weak Euler approximation. We prove weak convergence of the considered algorithm and present an in-depth analysis of how its error and computational cost depend on the jump activity level. Results of some numerical experiments, including pricing of barrier basket currency options, are presented.
