相关论文: Deep ReLU Network Expression Rates for Option Pric…

Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…

Numerical experiments indicate that deep learning algorithms overcome the curse of dimensionality when approximating solutions of semilinear PDEs. For certain linear PDEs and semilinear PDEs with gradient-independent nonlinearities this has…

The expressiveness of deep neural network (DNN) is a perspective to understandthe surprising performance of DNN. The number of linear regions, i.e. pieces thata piece-wise-linear function represented by a DNN, is generally used to…

Unknown examples that are unseen during training often appear in real-world computer vision tasks, and an intelligent self-learning system should be able to differentiate between known and unknown examples. Open set recognition, which…

Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open…

In recent years, deep neural networks have been applied to obtain high performance of prediction, classification, and pattern recognition. However, the weights in these deep neural networks are difficult to be explained. Although a linear…

The expressive power of neural networks is important for understanding deep learning. Most existing works consider this problem from the view of the depth of a network. In this paper, we study how width affects the expressiveness of neural…

Understanding the computational complexity of training simple neural networks with rectified linear units (ReLUs) has recently been a subject of intensive research. Closing gaps and complementing results from the literature, we present…

Deep reinforcement learning (RL) algorithms have recently achieved remarkable successes in various sequential decision making tasks, leveraging advances in methods for training large deep networks. However, these methods usually require…

We consider a stochastic volatility model with L\'evy jumps for a log-return process $Z=(Z_{t})_{t\geq 0}$ of the form $Z=U+X$, where $U=(U_{t})_{t\geq 0}$ is a classical stochastic volatility process and $X=(X_{t})_{t\geq 0}$ is an…

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem…

Recently, it has been proposed in the literature to employ deep neural networks (DNNs) together with stochastic gradient descent methods to approximate solutions of PDEs. There are also a few results in the literature which prove that DNNs…

In this article we study high-dimensional approximation capacities of shallow and deep artificial neural networks (ANNs) with the rectified linear unit (ReLU) activation. In particular, it is a key contribution of this work to reveal that…

Deep neural networks (DNNs) have been shown lack of robustness for the vulnerability of their classification to small perturbations on the inputs. This has led to safety concerns of applying DNNs to safety-critical domains. Several…

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…

This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…

We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size…

We introduce Direct Value Optimization (DVO), an innovative reinforcement learning framework for enhancing large language models in complex reasoning tasks. Unlike traditional methods relying on preference labels, DVO utilizes value signals…

Consider a discrete finite-dimensional, Markovian market model. In this setting, discretely sampled American options can be priced using the so-called ``non-recombining'' tree algorithm. By successively increasing the number of exercise…

Financial returns are known to exhibit heavy tails, volatility clustering and abrupt jumps that are poorly captured by classical diffusion models. Advances in machine learning have enabled highly flexible functional forms for conditional…