Related papers: Hedging with memory: shallow and deep learning wit…

We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called…

This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and…

Signature is an infinite graded sequence of statistics known to characterize geometric rough paths, which includes the paths with bounded variation. This object has been studied successfully for machine learning with mostly applications in…

Stochastic momentum methods have been widely adopted in training deep neural networks. However, their theoretical analysis of convergence of the training objective and the generalization error for prediction is still under-explored. This…

We present a unified framework for computing CVA sensitivities, hedging the CVA, and assessing CVA risk, using probabilistic machine learning meant as refined regression tools on simulated data, validatable by low-cost companion Monte Carlo…

In this paper, we propose a new first-order gradient-based algorithm to train deep neural networks. We first introduce the sign operation of stochastic gradients (as in sign-based methods, e.g., SIGN-SGD) into ADAM, which is called as…

Signature, lying at the heart of rough path theory, is a central tool for analysing controlled differential equations driven by irregular paths. Recently it has also found extensive applications in machine learning and data science as a…

Trend change prediction in complex systems with a large number of noisy time series is a problem with many applications for real-world phenomena, with stock markets as a notoriously difficult to predict example of such systems. We approach…

In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial…

We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a…

Traditional approaches to estimating beta in finance often involve rigid assumptions and fail to adequately capture beta dynamics, limiting their effectiveness in use cases like hedging. To address these limitations, we have developed a…

Bayesian neural networks allow us to keep track of uncertainties, for example in top tagging, by learning a tagger output together with an error band. We illustrate the main features of Bayesian versions of established deep-learning…

We provide an introduction to the topic of path signatures as means of feature extraction for machine learning from data streams. The article stresses the mathematical theory underlying the signature methodology, highlighting the conceptual…

Hedging in the presence of transaction costs leads to complex optimization problems. These problems typically lack closed-form solutions, and their implementation relies on numerical methods that provide hedging strategies for specific…

We consider the supervised learning problem of learning the price of an option or the implied volatility given appropriate input data (model parameters) and corresponding output data (option prices or implied volatilities). The majority of…

The objectives of option hedging/trading extend beyond mere protection against downside risks, with a desire to seek gains also driving agent's strategies. In this study, we showcase the potential of robust risk-aware reinforcement learning…

Deep learning searches for nonlinear factors for predicting asset returns. Predictability is achieved via multiple layers of composite factors as opposed to additive ones. Viewed in this way, asset pricing studies can be revisited using…

Hedging a portfolio containing autocallable notes presents unique challenges due to the complex risk profile of these financial instruments. In addition to hedging, pricing these notes, particularly when multiple underlying assets are…