Related papers: Enhancing Black-Scholes Delta Hedging via Deep Lea…

Despite the power of deep neural networks for a wide range of tasks, an overconfident prediction issue has limited their practical use in many safety-critical applications. Many recent works have been proposed to mitigate this issue, but…

Error backpropagation is a highly effective mechanism for learning high-quality hierarchical features in deep networks. Updating the features or weights in one layer, however, requires waiting for the propagation of error signals from…

We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Levy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency…

Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…

Whereas cognitive models of learning often assume direct experience with both the features of an event and with a true label or outcome, much of everyday learning arises from hearing the opinions of others, without direct access to either…

The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually converges slowly. To speed up the convergence of this…

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…

One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based…

Stock trading strategy plays a crucial role in investment companies. However, it is challenging to obtain optimal strategy in the complex and dynamic stock market. We explore the potential of deep reinforcement learning to optimize stock…

We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The…

Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. The Black-Scholes option pricing model is one of the most widely used models by…

Artificial Intelligence algorithms have been steadily increasing in popularity and usage. Deep Learning, allows neural networks to be trained using huge datasets and also removes the need for human extracted features, as it automates the…

Deep learning methods dominate short-term high-resolution precipitation nowcasting in terms of prediction error. However, their operational usability is limited by difficulties explaining dynamics behind the predictions, which are smoothed…

Attention Residuals replace standard additive residual connections with learned softmax attention over previous layer outputs, enabling selective cross-layer routing. However, standard Attention Residuals still attend over cumulative hidden…

Optimal stopping is the problem of deciding the right time at which to take a particular action in a stochastic system, in order to maximize an expected reward. It has many applications in areas such as finance, healthcare, and statistics.…

We have applied a Long Short-Term Memory neural network to model S&P 500 volatility, incorporating Google domestic trends as indicators of the public mood and macroeconomic factors. In a held-out test set, our Long Short-Term Memory model…

Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…

As the complexity and dynamism of financial markets continue to grow, traditional financial risk prediction methods increasingly struggle to handle large datasets and intricate behavior patterns. This paper explores the feasibility and…

We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European,…

We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…