Related papers: Deep Stochastic Optimization in Finance
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…
This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…
The development of new classification and regression algorithms based on empirical risk minimization (ERM) over deep neural network hypothesis classes, coined deep learning, revolutionized the area of artificial intelligence, machine…
We study the problem of excess risk evaluation for empirical risk minimization (ERM) under convex losses. We show that by leveraging the idea of wild refitting, one can upper bound the excess risk through the so-called "wild optimism,"…
Big data, both in its structured and unstructured formats, have brought in unforeseen challenges in economics and business. How to organize, classify, and then analyze such data to obtain meaningful insights are the ever-going research…
One of the most fundamental questions in quantitative finance is the existence of continuous-time diffusion models that fit market prices of a given set of options. Traditionally, one employs a mix of intuition, theoretical and empirical…
The aim of this study is to devise numerical methods for dealing with very high-dimensional Bermudan-style derivatives. For such problems, we quickly see that we can at best hope for price bounds, and we can only use a simulation approach.…
The ability to construct a realistic simulator of financial exchanges, including reproducing the dynamics of the limit order book, can give insight into many counterfactual scenarios, such as a flash crash, a margin call, or changes in…
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the…
Managing stock efficiently remains a core issue in modern logistics, where companies must reconcile cost efficiency with dependable service despite unpredictable market conditions. Conventional models often overlook the direct connection…
Recursive Marginal Quantization (RMQ) allows fast approximation of solutions to stochastic differential equations in one-dimension. When applied to two factor models, RMQ is inefficient due to the fact that the optimization problem is…
This survey (re)introduces reinforcement learning methods to economists. The curse of dimensionality limits how far exact dynamic programming can be effectively applied, forcing us to rely on suitably "small" problems or our ability to…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the…
Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
Portfolio optimization has been a central problem in finance, often approached with two steps: calibrating the parameters and then solving an optimization problem. Yet, the two-step procedure sometimes encounter the "error maximization"…
With the recent advancements in machine learning (ML), artificial neural networks (ANN) are starting to play an increasingly important role in quantitative finance. Dynamic portfolio optimization is among many problems that have…
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…
In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by $U$-statistics of degree $d\geq 1$, i.e. functionals of the training data with low variance…