Related papers: Improved model-free bounds for multi-asset options…
The ability to train randomly initialised deep neural networks is known to depend strongly on the variance of the weight matrices and biases as well as the choice of nonlinear activation. Here we complement the existing geometric analysis…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
Risk assessment and in particular derivatives pricing is one of the core areas in computational finance and accounts for a sizeable fraction of the global computing resources of the financial industry. We outline a quantum-inspired…
Model selection is a problem that has occupied machine learning researchers for a long time. Recently, its importance has become evident through applications in deep learning. We propose an agreement-based learning framework that prevents…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
Reinforcement Learning is divided in two main paradigms: model-free and model-based. Each of these two paradigms has strengths and limitations, and has been successfully applied to real world domains that are appropriate to its…
Accurate option pricing is essential for effective trading and risk management in financial markets, yet it remains challenging due to market volatility and the limitations of traditional models like Black-Scholes. In this paper, we…
Deep neural networks (DNNs) have garnered significant attention in financial asset pricing, due to their strong capacity for modeling complex nonlinear relationships within financial data. However, sophisticated models are prone to…
Deep neural network models owe their representational power to the high number of learnable parameters. It is often infeasible to run these largely parametrized deep models in limited resource environments, like mobile phones. Network…
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive…
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…
We consider a novel formulation of the dynamic pricing and demand learning problem, where the evolution of demand in response to posted prices is governed by a stochastic variant of the popular Bass model with parameters $\alpha, \beta$…
In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the…
An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a complete market with a finite number of…
The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here, we analyze the duality principle for options that…
In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the…
Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using…
The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete…
This paper outlines, and through stylized examples evaluates a novel and highly effective computational technique in quantitative finance. Empirical Risk Minimization (ERM) and neural networks are key to this approach. Powerful open source…
In this work, we study the learning theory of reward modeling with pairwise comparison data using deep neural networks. We establish a novel non-asymptotic regret bound for deep reward estimators in a non-parametric setting, which depends…