scholarly journals Exponential integrability properties of Euler discretization schemes for the Cox--Ingersoll--Ross process

2016 ◽  
Vol 21 (10) ◽  
pp. 3359-3377 ◽  
Author(s):  
Christoph Reisinger ◽  
Andrei Cozma
Keyword(s):  
Exponential Integrability ◽  
Discretization Schemes ◽  
Euler Discretization

Spatial Discretization Schemes

THERMOPEDIA ◽  
2008 ◽  
Author(s):  
Pedro J. Coelho
Keyword(s):  
Spatial Discretization ◽  
Discretization Schemes

Implicit time discretization schemes for mixed least-squares finite element formulations

2020 ◽  
Vol 368 ◽  
pp. 113111
Author(s):  
Solveigh Averweg ◽  
Alexander Schwarz ◽  
Carina Nisters ◽  
Jörg Schröder
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Time Discretization ◽  
Implicit Time ◽  
Discretization Schemes ◽  
Finite Element Formulations

scholarly journals A LOW-BIAS SIMULATION SCHEME FOR THE SABR STOCHASTIC VOLATILITY MODEL

2012 ◽  
Vol 15 (02) ◽  
pp. 1250016 ◽  
Author(s):  
BIN CHEN ◽  
CORNELIS W. OOSTERLEE ◽  
HANS VAN DER WEIDE
Keyword(s):  
Stochastic Volatility ◽  
Asset Price ◽  
Realistic Model ◽  
Stochastic Volatility Model ◽  
Model Parameters ◽  
Fixed Income ◽  
Financial Industry ◽  
Volatility Model ◽  
Discretization Schemes ◽  
Simulation Scheme

The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.

scholarly journals Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation

2018 ◽  
Vol 52 (2) ◽  
pp. 567-593 ◽  
Author(s):  
Li Chen ◽  
Simone Göttlich ◽  
Stephan Knapp
Keyword(s):  
Particle System ◽  
Rigorous Derivation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Delta Potential ◽  
Intermediate Particle ◽  
Stochastic Particle System ◽  
Aggregation Equation ◽  
Discretization Schemes ◽  
Theoretical Results

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a stochastic particle system while introducing an intermediate particle system with smooth interaction potential. The theoretical results are compared to numerical simulations relying on suitable discretization schemes for the microscopic and macroscopic level. In particular, the regime switch where the analytic theory fails is numerically analyzed very carefully and allows for a better understanding of the equation.

Dynamic Euler Discretization of Exploding Processes

2021 ◽  
Author(s):  
Gael Mboussa Anga
Keyword(s):  
Euler Discretization

Comparison of Various Discretization Schemes for Simulation of Large Field Case Reservoirs Using Unstructured Grids

2021 ◽  
Author(s):  
Samier Pierre ◽  
Raguenel Margaux ◽  
Darche Gilles
Keyword(s):  
Large Scale ◽  
Unstructured Grids ◽  
Computational Cost ◽  
Large Field ◽  
Real Field ◽  
Test Case ◽  
Generation Task ◽  
Field Case ◽  
Flux Approximation ◽  
Discretization Schemes

Abstract Solving the equations governing multiphase flow in geological formations involves the generation of a mesh that faithfully represents the structure of the porous medium. This challenging mesh generation task can be greatly simplified by the use of unstructured (tetrahedral) grids that conform to the complex geometric features present in the subsurface. However, running a million-cell simulation problem using an unstructured grid on a real, faulted field case remains a challenge for two main reasons. First, the workflow typically used to construct and run the simulation problems has been developed for structured grids and needs to be adapted to the unstructured case. Second, the use of unstructured grids that do not satisfy the K-orthogonality property may require advanced numerical schemes that preserve the accuracy of the results and reduce potential grid orientation effects. These two challenges are at the center of the present paper. We describe in detail the steps of our workflow to prepare and run a large-scale unstructured simulation of a real field case with faults. We perform the simulation using four different discretization schemes, including the cell-centered Two-Point and Multi-Point Flux Approximation (respectively, TPFA and MPFA) schemes, the cell- and vertex-centered Vertex Approximate Gradient (VAG) scheme, and the cell- and face-centered hybrid Mimetic Finite Difference (MFD) scheme. We compare the results in terms of accuracy, robustness, and computational cost to determine which scheme offers the best compromise for the test case considered here.

Sign in / Sign up

Export Citation Format

Share Document