摘要翻译：
本文应用Kuznetsov等人最近建立的Wiener-Hopf Monte Carlo(WHMC)模拟Levy过程的方法。[17]路径函数，特别是第一次通过时间、过冲、下冲和通过时间之前的最后一个最大值。这些函数有许多应用，例如在金融（利维模型中奇异期权的定价）和保险（利维保险风险过程的破产时间、破产时的债务和相关数量）中。该技术适用于任何Levy过程，其运行的下确界和上确界在一个独立的指数时间内计算，允许从。这包括经典的例子，如稳定过程，谱单边Levy过程的子类和大的新家族，如亚纯Levy过程。最后给出了一些例子。所说明的一个具体方面是，WHMC模拟技术在近似第一次通过时间方面比基于Levy过程抽样增量的“普通”蒙特卡罗模拟技术表现得更好。
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英文标题：
《Applying the Wiener-Hopf Monte Carlo simulation technique for Levy
processes to path functionals such as first passage times, undershoots and
overshoots》
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作者：
Albert Ferreiro-Castilla and Kees van Schaik
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最新提交年份：
2014
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Levy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have many applications, for instance in finance (the pricing of exotic options in a Levy model) and insurance (ruin time, debt at ruin and related quantities for a Levy insurance risk process). The technique works for any Levy process whose running infimum and supremum evaluated at an independent exponential time allows sampling from. This includes classic examples such as stable processes, subclasses of spectrally one sided Levy processes and large new families such as meromorphic Levy processes. Finally we present some examples. A particular aspect that is illustrated is that the WHMC simulation technique performs much better at approximating first passage times than a `plain\' Monte Carlo simulation technique based on sampling increments of the Levy process.
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