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Backward stochastic differential equation (BSDE)-based deep learning methods provide an alternative to Physics-Informed Neural Networks (PINNs) for solving high-dimensional partial differential equations (PDEs), offering potential…
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…
We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on…
This paper proposes a Deep Reinforcement Learning algorithm for financial portfolio trading based on Deep Q-learning. The algorithm is capable of trading high-dimensional portfolios from cross-sectional datasets of any size which may…
We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex Lipschitz continuous reward functions, we give a…
Option pricing is a significant problem for option risk management and trading. In this article, we utilize a framework to present financial data from different sources. The data is processed and represented in a form of 2D tensors in three…
In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional It\^o (or path-dependent) calculus, the relationship between the systems and related path-dependent…
This thesis provides an overview of the recent advances in reinforcement learning in pricing and hedging financial instruments, with a primary focus on a detailed explanation of the Q-Learning Black Scholes approach, introduced by Halperin…
We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal…
We derive a tight analysis of the trade-off function for Differentially Private Stochastic Gradient Descent (DP-SGD) with subsampling based on random shuffling within the $f$-DP framework. Our analysis covers the regime $\sigma \geq…
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from…
We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReLU architectures capable of efficiently approximating tensor…
We present a robust Deep Hedging framework for the pricing and hedging of option portfolios that significantly improves training efficiency and model robustness. In particular, we propose a neural model for training model embeddings which…
The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equations (BSDE) and…
This paper studies the equal risk pricing (ERP) framework for the valuation of European financial derivatives. This option pricing approach is consistent with global trading strategies by setting the premium as the value such that the…
We propose a new method, called a deep-genetic algorithm (deep-GA), to accelerate the performance of the so-called deep-BSDE method, which is a deep learning algorithm to solve high dimensional partial differential equations through their…
Forecasting stock market direction is always an amazing but challenging problem in finance. Although many popular shallow computational methods (such as Backpropagation Network and Support Vector Machine) have extensively been proposed,…
We present a reinforcement-learning (RL) framework for dynamic hedging of equity index option exposures under realistic transaction costs and position limits. We hedge a normalized option-implied equity exposure (one unit of underlying…
This paper tackles the problem of feature selection in a highly challenging setting: $\mathbb{E}(y | \boldsymbol{x}) = G(\boldsymbol{x}_{\mathcal{S}_0})$, where $\mathcal{S}_0$ is the set of relevant features and $G$ is an unknown,…
An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the securities lending market. Because of haircuts, she posts additional…