中文摘要：

这份报纸证实有二修改的一个格子 Boltzmann 方法(LBM ) 为解决在亚洲人和 lookback 选择定价产生的部分微分方程(PDE ) 工作。股票价格的时间进化能被认为是使随机化的运动在不同方向的粒子，和 LBM 的分离计划能作为二项式的模型被解释。与 Chapman-Enskog 多尺度的扩大， PDE 从连续 Boltzmann 方程正确地被恢复，计算复杂性是 O (N) ，在 N 是空间节点的数字的地方。比作传统的 LBM，平衡分发的系数和修改功能作为多项式被拿而不是常数。LBM 的稳定性经由数字例子被学习，数字比较证明 LBM 象存在一样精确为定价的数字方法异国情调的选择并且花少得多中央处理器时间。

英文摘要：

This paper establishes a lattice Boltzmann method （LBM） with two amending functions for solving partial differential equations （PDEs） arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O（N）, where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.