标题： 无偏扩散过程蒙特卡罗模拟 显示英文标题

标题： Unbiased Monte Carlo Simulation of Diffusion Processes

摘要： 蒙特卡洛模拟扩散过程通常由于时间离散化而在最终结果中引入偏差。 使用辅助泊松过程，可以运行无偏的模拟。 在本文中，我们提出了一种蒙特卡洛方案，该方案收敛于精确值。 我们设法在所有情况下保持模拟方差有限，因此大数定律保证了收敛性。 此外，模拟噪声是泊松过程强度的递减函数。 我们的方法处理具有非常数漂移和非常数方差-协方差矩阵的多维过程。 它还涵盖了随机利率。 显示英文摘要

摘要： Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such a Monte Carlo scheme which converges to the exact value. We manage to keep the simulation variance finite in all cases, so that the strong law of large numbers guarantees the convergence. Moreover, the simulation noise is a decreasing function of the Poisson process intensity. Our method handles multidimensional processes with nonconstant drifts and nonconstant variance-covariance matrices. It also encompasses stochastic interest rates.