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We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We analyze the consistency of the SAA optimal values and SAA…

Optimization and Control · Mathematics 2023-08-03 Johannes Milz

In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…

Methodology · Statistics 2023-10-27 Kimia Vahdat , Sara Shashaani

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…

This paper develops a flexible approach to predict the price effects of horizontal mergers using ML/AI methods. While standard merger simulation techniques rely on restrictive assumptions about firm conduct, we propose a data-driven…

Econometrics · Economics 2025-06-06 Harold D. Chiang , Jack Collison , Lorenzo Magnolfi , Christopher Sullivan

Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…

Mathematical Physics · Physics 2013-12-24 Yannis Pantazis , Markos Katsoulakis

In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…

Computational Finance · Quantitative Finance 2015-03-19 Giacomo Bormetti , Sofia Cazzaniga

Identifying meaningful relationships between the price movements of financial assets is a challenging but important problem in a variety of financial applications. However with recent research, particularly those using machine learning and…

Statistical Finance · Quantitative Finance 2022-02-21 Rian Dolphin , Barry Smyth , Ruihai Dong

Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…

Pricing of Securities · Quantitative Finance 2012-05-15 Jean-Pierre Fouque , Sebastian Jaimungal , Matthew Lorig

The reliability of kinetic Monte Carlo (KMC) simulations depends on accurate transition rates. The self-learning KMC method (Trushin et al 2005 Phys. Rev. B 72 115401) combines the accuracy of rates calculated from a realistic potential…

Materials Science · Physics 2013-01-01 A. Latz , L. Brendel , D. E. Wolf

Modern evolvements of the technologies have been leading to a profound influence on the financial market. The introduction of constituents like Exchange-Traded Funds, and the wide-use of advanced technologies such as algorithmic trading,…

Statistical Finance · Quantitative Finance 2021-08-20 Liao Zhu

Discretely sampled variance and volatility swaps trade actively in OTC markets. To price these swaps, the continuously sampled approximation is often used to simplify the computations. The purpose of this paper is to study the conditions…

Probability · Mathematics 2011-03-08 Robert Jarrow , Younes Kchia , Martin Larsson , Philip Protter

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie…

Computational Finance · Quantitative Finance 2020-09-28 Ljudmila A. Bordag

We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…

Portfolio Management · Quantitative Finance 2009-09-23 Michael J. Neely

In this article, we present a method for approximating affine processes on the cone of positive Hilbert-Schmidt operators using matrix-valued affine processes. By leveraging results from the theory on affine processes with values in the…

Probability · Mathematics 2023-01-18 Sven Karbach

In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading…

Pricing of Securities · Quantitative Finance 2020-06-16 Kevin S. Zhang , Traian A. Pirvu

A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model…

Numerical Analysis · Mathematics 2021-10-05 Andreas Binder , Onkar Jadhav , Volker Mehrmann

We review the assumptions on which the Monte Carlo renormalization technique is based, in particular the analyticity of the block spin transformations. On this basis, we select an optimized Kadanoff blocking rule in combination with the…

Condensed Matter · Physics 2016-08-15 H. W. J. Blöte , J. R. Heringa , A. Hoogland , E. W. Meyer , T. S. Smit

We applied Deep Q-Network with a Convolutional Neural Network function approximator, which takes stock chart images as input, for making global stock market predictions. Our model not only yields profit in the stock market of the country…

General Finance · Quantitative Finance 2019-11-27 Jinho Lee , Raehyun Kim , Yookyung Koh , Jaewoo Kang

In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…

Numerical Analysis · Mathematics 2024-10-24 Sebastian Becker , Arnulf Jentzen , Marvin S. Müller , Philippe von Wurstemberger

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or…

Computational Finance · Quantitative Finance 2015-09-14 Edgardo Brigatti , Felipe Macias , Max O. Souza , Jorge P. Zubelli