Related papers: Deep Learning Algorithms for Hedging with Friction…
We present a method for finding optimal hedging policies for arbitrary initial portfolios and market states. We develop a novel actor-critic algorithm for solving general risk-averse stochastic control problems and use it to learn hedging…
The Black-Scholes model, defined under the assumption of a perfect financial market, theoretically creates a flawless hedging strategy allowing the trader to evade risks in a portfolio of options. However, the concept of a "perfect…
This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely…
It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…
Derivative hedging and pricing are important and continuously studied topics in financial markets. Recently, deep hedging has been proposed as a promising approach that uses deep learning to approximate the optimal hedging strategy and can…
Using techniques from deep learning (cf. [B\"uh+19]), we show that neural networks can be trained successfully to replicate the modified payoff functions that were first derived in the context of partial hedging by [FL00]. Not only does…
Transfer learning has become an essential technique for utilizing information from source datasets to improve the performance of the target task. However, in the context of high-dimensional data, heterogeneity arises due to heteroscedastic…
Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…
We propose a deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and high-dimensional forward-backward stochastic differential equations with jumps (FBSDEJs), where the jump-diffusion…
We propose a Stochastic Gradient Descent (SGD)-type algorithm for Personalized Federated Learning which can be particularly attractive for mobile energy-limited regimes due to its low per-client computational cost. The model to be trained…
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…
This paper treats the Merton problem how to invest in safe assets and risky assets to maximize an investor's utility, given by investment opportunities modeled by a $d$-dimensional state process. The problem is represented by a partial…
In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…
Most deep learning models are based on deep neural networks with multiple layers between input and output. The parameters defining these layers are initialized using random values and are "learned" from data, typically using stochastic…
We study the capability of arbitrage-free neural-SDE market models to yield effective strategies for hedging options. In particular, we derive sensitivity-based and minimum-variance-based hedging strategies using these models and examine…
Mathematical modelling is ubiquitous in the financial industry and drives key decision processes. Any given model provides only a crude approximation to reality and the risk of using an inadequate model is hard to detect and quantify. By…
In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimization of non-convex loss functions. Since the pioneering work of…
The increasing complexity of deep learning models and the demand for processing vast amounts of data make the utilization of large-scale distributed systems for efficient training essential. These systems, however, face significant…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…