论文标题
多级蒙特卡洛及其在金融工程中的应用
Multilevel Monte Carlo and its Applications in Financial Engineering
论文作者
论文摘要
在本文中，我们在金融工程应用程序的范式中介绍了有关多层次蒙特卡洛（MLMC）算法的最新发展。我们特别关注在两个亚地区进行的最新研究，即期权定价和财务风险管理。对于前者而言，讨论涉及将重要性采样算法纳入与MLMC估计器的结合，从而构建了混合算法，以便为估算器的整体差异降低。在后者的情况下，我们讨论了为构建有效算法而进行的研究，以便以有效的方式估算价值风险（VAR）和条件VAR（CVAR）的风险度量。在这方面，我们简要讨论了自适应抽样算法的动机和构建，目的是有效估计嵌套的期望，这通常在计算上昂贵。
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two subareas, namely, option pricing and financial risk management. For the former, the discussion involves incorporation of the importance sampling algorithm, in conjunction with the MLMC estimator, thereby constructing a hybrid algorithm in order to achieve reduction for the overall variance of the estimator. In case of the latter, we discuss the studies carried out in order to construct an efficient algorithm in order to estimate the risk measures of Value-at-Risk (VaR) and Conditional Var (CVaR), in an efficient manner. In this regard, we briefly discuss the motivation and the construction of an adaptive sampling algorithm with an aim to efficiently estimate the nested expectation, which, in general is computationally expensive.
