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Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the…

Machine Learning · Computer Science 2025-10-07 Jinyang Jiang , Bernd Heidergott , Jiaqiao Hu , Yijie Peng

Applications of the quantum algorithm for Monte Carlo simulation to pricing of financial derivatives have been discussed in previous papers. However, up to now, the pricing model discussed in such papers is Black-Scholes model, which is…

Quantum Physics · Physics 2020-07-06 Kazuya Kaneko , Koichi Miyamoto , Naoyuki Takeda , Kazuyoshi Yoshino

The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…

Machine Learning · Computer Science 2020-04-03 Ke Li , Kejun Tang , Tianfan Wu , Qifeng Liao

We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…

Quantum Physics · Physics 2016-07-12 Iris Cong , Luming Duan

We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multiscale hyperbolic heat system with quantum algorithms (hence…

Numerical Analysis · Mathematics 2023-06-14 Shi Jin , Nana Liu , Yue Yu

We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as…

Computational Physics · Physics 2021-08-17 Roie Dann , Guy Elbaz , Jonathan Berkheim , Alan Muhafra , Omri Nitecki , Daniel Wilczynski , Nimrod Moiseyev

In this work, we present the methods necessary to price an important set of derivatives on a quantum device while offering an advantage over existing classical methods. The methods developed here, in conjunction with ~\cite{GumaroS2026},…

Quantum Physics · Physics 2026-05-29 Gumaro Rendon , Stepan Smid , Sarvagya Upadhyay

This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted…

Numerical Analysis · Mathematics 2017-01-24 X. G. Zhu , Y. F. Nie

In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…

Numerical Analysis · Mathematics 2024-11-04 Qiwei Feng

Markov decision models (MDM) used in practical applications are most often less complex than the underlying `true' MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what…

Optimization and Control · Mathematics 2019-09-18 Patrick Kern , Axel Simroth , Henryk Zähle

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an…

Statistical Mechanics · Physics 2008-12-02 Kirill Ilinski , Alexander Stepanenko

A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the…

Pricing of Securities · Quantitative Finance 2014-11-03 Xiaolin Luo , Pavel Shevchenko

This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…

Pricing of Securities · Quantitative Finance 2018-05-03 Foad Shokrollahi

Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…

Quantum Physics · Physics 2026-03-23 Jordan Cioni , Fabio Semperlotti

An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…

Computational Physics · Physics 2023-07-14 Timothy Meagher , Bin Jiang , Peng Jiang

We study the pricing problem for corporate defaultable bond from the viewpoint of the investors outside the firm that could not exactly know about the information of the firm. We consider the problem for pricing of corporate defaultable…

Pricing of Securities · Quantitative Finance 2013-07-09 Hyong-Chol O , Jong-Jun Jo , Chol-Ho Kim

Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can…

Risk Management · Quantitative Finance 2026-01-05 Pengpeng Li , Shi-Dong Liang

We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…

Numerical Analysis · Mathematics 2019-10-28 Jérôme Droniou , Robert Eymard , T. Gallouët , R. Herbin

Traditional machine learning methods have been widely studied in financial innovation. My study focuses on the application of deep learning methods on asset pricing. I investigate various deep learning methods for asset pricing, especially…

Statistical Finance · Quantitative Finance 2022-09-27 Chen Zhang