New Brownian bridge construction in quasi-Monte Carlo methods for computational finance

AbstractQuasi-Monte Carlo (QMC) methods have been playing an important role for high-dimensional problems in computational finance. Several techniques, such as the Brownian bridge (BB) and the principal component analysis, are often used in QMC as possible ways to improve the performance of QMC. This paper proposes a new BB construction, which enjoys some interesting properties that appear useful in QMC methods. The basic idea is to choose the new step of a Brownian path in a certain criterion such that it maximizes the variance explained by the new variable while holding all previously chosen steps fixed. It turns out that using this new construction, the first few variables are more “important” (in the sense of explained variance) than those in the ordinary BB construction, while the cost of the generation is still linear in dimension. We present empirical studies of the proposed algorithm for pricing high-dimensional Asian options and American options, and demonstrate the usefulness of the new BB

High-Performance Inference Graph Convolutional Networks for Skeleton-Based Action Recognition

Recently, significant achievements have been made in skeleton-based human action recognition with the emergence of graph convolutional networks (GCNs). However, the state-of-the-art (SOTA) models used for this task focus on constructing more complex higher-order connections between joint nodes to describe skeleton information, which leads to complex inference processes and high computational costs, resulting in reduced model's practicality. To address the slow inference speed caused by overly complex model structures, we introduce re-parameterization and over-parameterization techniques to GCNs, and propose two novel high-performance inference graph convolutional networks, namely HPI-GCN-RP and HPI-GCN-OP. HPI-GCN-RP uses re-parameterization technique to GCNs to achieve a higher inference speed with competitive model performance. HPI-GCN-OP further utilizes over-parameterization technique to bring significant performance improvement with inference speed slightly decreased. Experimental results on the two skeleton-based action recognition datasets demonstrate the effectiveness of our approach. Our HPI-GCN-OP achieves an accuracy of 93% on the cross-subject split of the NTU-RGB+D 60 dataset, and 90.1% on the cross-subject benchmark of the NTU-RGB+D 120 dataset and is 4.5 times faster than HD-GCN at the same accuracy

Exploratory mean-variance portfolio selection with Choquet regularizers

In this paper, we study a continuous-time exploratory mean-variance (EMV) problem under the framework of reinforcement learning (RL), and the Choquet regularizers are used to measure the level of exploration. By applying the classical Bellman principle of optimality, the Hamilton-Jacobi-Bellman equation of the EMV problem is derived and solved explicitly via maximizing statically a mean-variance constrained Choquet regularizer. In particular, the optimal distributions form a location-scale family, whose shape depends on the choices of the Choquet regularizer. We further reformulate the continuous-time Choquet-regularized EMV problem using a variant of the Choquet regularizer. Several examples are given under specific Choquet regularizers that generate broadly used exploratory samplers such as exponential, uniform and Gaussian. Finally, we design a RL algorithm to simulate and compare results under the two different forms of regularizers