Related papers: Isogeometric analysis in option pricing
We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…
We study the problem of optimal pricing and hedging of a European option written on an illiquid asset $Z$ using a set of proxies: a liquid asset $S$, and $N$ liquid European options $P_i$, each written on a liquid asset $Y_i, i=1,N$. We…
We consider the isogeometric analysis for fractional PDEs involving the fractional Laplacian in two dimensions. An isogeometric collocation method is developed to discretize the fractional Laplacian and applied to the fractional Poisson…
In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation…
In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…
During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
This article considers the NURBS-Enhanced Finite Element Method (NEFEM) applied to the compressible Navier-Stokes equations. NEFEM, in contrast to conventional finite element formulations, utilizes a NURBS-based computational domain…
Ensemble learning is characterized by flexibility, high precision, and refined structure. As a critical component within computational finance, option pricing with machine learning requires both high predictive accuracy and reduced…
We introduce a novel quadrature strategy for Isogeometric Analysis (IgA) boundary element discretizations, specifically tailored to collocation methods. Thanks to the dimensionality reduction and the natural handling of unbounded domains,…
We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hilbert space of real-valued function on the positive real…
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and…
Isogeometric Analysis (IgA) is a versatile method for the discretization of partial differential equations on complex domains, which arise in various applications of science and engineering. Some complex geometries can be better described…
We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the…
This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…
This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is formulated by introducing a tracking-type cost functional…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.