论文标题
通过破坏性高斯近似值模拟降水及其持续时间
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation
论文作者
论文摘要
我们开发了一种计算方法，用于缩水的预期功能及其在指数lévy模型中的持续时间。它基于一种针对国家联合定律的新型仿真算法，至上和时间是由一般莱维过程的高斯近似实现的。我们绑定了各种本地Lipschitz的偏见和应用在应用中产生的不连续的回报，并分析相应的蒙特卡洛和多层次蒙特卡洛估计器的计算复杂性。已经分析了Lipschitz收益的Lévy过程的蒙特卡洛方法（使用高斯近似），在这种情况下，当跳跃活动较高时，我们算法的计算复杂性高达两个数量级。我们方法的核心是某些Wasserstein距离上的边界，这是通过新型的SBG耦合在Lévy过程及其高斯近似之间获得的。基于专用的GitHub存储库中实现的数值性能，与我们的理论界限达成了很好的一致性。
We develop a computational method for expected functionals of the drawdown and its duration in exponential Lévy models. It is based on a novel simulation algorithm for the joint law of the state, supremum and time the supremum is attained of the Gaussian approximation of a general Lévy process. We bound the bias for various locally Lipschitz and discontinuous payoffs arising in applications and analyse the computational complexities of the corresponding Monte Carlo and multilevel Monte Carlo estimators. Monte Carlo methods for Lévy processes (using Gaussian approximation) have been analysed for Lipschitz payoffs, in which case the computational complexity of our algorithm is up to two orders of magnitude smaller when the jump activity is high. At the core of our approach are bounds on certain Wasserstein distances, obtained via the novel SBG coupling between a Lévy process and its Gaussian approximation. Numerical performance, based on the implementation in the dedicated GitHub repository, exhibits a good agreement with our theoretical bounds.
