Faster Comparison of Stopping Times by Nested Conditional Monte Carlo

嵌套最优传输距离

Nested Optimal Transport Distances

针对金融时间序列生成模型评估缺乏共识指标的问题，提出采用嵌套最优传输距离作为鲁棒评估指标，并设计了一种统计一致且可并行化的高效计算算法，显著加速了计算过程。

一种用于最优停时问题的深度原始-对偶BSDE方法

A deep primal-dual BSDE method for optimal stopping problems

本研究提出基于停时迭代的深度原始-对偶BSDE框架求解最优停时问题，设计含鞅部分的新型损失函数降方差缓误差，以非嵌套蒙特卡洛得最优值真实上界，在美式期权定价中可直接输出对冲比率。

Sample Recycling for Nested Simulation with Application in Portfolio Risk Measurement

Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates outer scenarios and the inner-level simulations are run in each outer scenario to estimate the corresponding conditional expectation. The resulting sample of conditional expectations is then used to estimate different risk measures of interest. Despite its flexibility, nested simulation is notorious for its heavy computational burden. We introduce a novel simulation procedure that reuses inner simulation outputs to improve efficienc…

Multilevel nested simulation for efficient risk estimation

We investigate the problem of computing a nested expectation of the form $\mathbb{P}[\mathbb{E}[X|Y] \!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])]$ where $\textrm{H}$ is the Heaviside function. This nested expectation appears, for example, when estimating the probability of a large loss from a financial portfolio. We present a method that combines the idea of using Multilevel Monte Carlo (MLMC) for nested expectations with the idea of adaptively selecting the number of samples in the approximation of the inner expectation, as proposed by (Broadie et al., 2011). We propose and analyse …

Least Squares Monte Carlo applied to Dynamic Monetary Utility Functions

In this paper we explore ways of numerically computing recursive dynamic monetary risk measures and utility functions. Computationally, this problem suffers from the curse of dimensionality and nested simulations are unfeasible if there are more than two time steps. The approach considered in this paper is to use a Least Squares Monte Carlo (LSM) algorithm to tackle this problem, a method which has been primarily considered for valuing American derivatives, or more general stopping time problems, as these also give rise to backward recursions with corresponding challenges in terms of numerical…