Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motion

DOI10.1016/j.cam.2021.113951zbMath1490.60209arXiv2003.10193OpenAlexW4200101867MaRDI QIDQ2074883

Irene Tubikanec, Massimiliano Tamborrino, Evelyn Buckwar, Petr Lansky

Publication date: 11 February 2022

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.10193

zbMATH Keywords

GARCH modelboundary preservationFeller's boundary classificationlog-ODE methodmoment preservationnumerical splitting schemes

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (5)

A splitting method for SDEs with locally Lipschitz drift: illustration on the FitzHugh-Nagumo model ⋮ A long term analysis of stochastic theta methods for mean reverting linear process with jumps ⋮ Exact solution of interacting particle systems related to random matrices ⋮ Numerical conservation issues for jump Pearson diffusions ⋮ High Order Splitting Methods for SDEs Satisfying a Commutativity Condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mean-square stability analysis of numerical schemes for stochastic differential systems
• High-order approximation of Pearson diffusion processes
• A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems
• A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods
• Splitting and composition methods for explicit time dependence in separable dynamical systems
• A stochastic version of the jansen and rit neural mass model: analysis and numerics
• On weak approximations of \((a, b)\)-invariant diffusions
• The effect of mean reversion on investment under uncertainty
• An option pricing formula for the GARCH diffusion model
• Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Mean-square stability of numerical schemes for stochastic differential systems
• A real options approach to the valuation of a forestry investment.
• On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity
• The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations
• Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs
• Analysis of some splitting schemes for the stochastic Allen-Cahn equation
• Molecular dynamics. With deterministic and stochastic numerical methods
• On the relation between ordinary and stochastic differential equations
• A boundary preserving numerical scheme for the Wright-Fisher model
• Structure preserving stochastic integration schemes in interest rate derivative modeling
• Two singular diffusion problems
• A Lie Algebraic Approach to Numerical Integration of Stochastic Differential Equations
• A non-standard-Euler–Maruyama scheme
• Splitting Integrators for the Stochastic Landau--Lifshitz Equation
• CHI-SQUARE SIMULATION OF THE CIR PROCESS AND THE HESTON MODEL
• An Introduction to Statistical Computing
• A Theory of the Term Structure of Interest Rates
• Estimation of the input parameters in the Feller neuronal model
• Stochastic Differential Equations in Infinite Dimensions
• Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations
• On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
• On the Product of Semi-Groups of Operators
• On the discretization schemes for the CIR (and Bessel squared) processes
• Splitting methods
• Boundary Preserving Semianalytic Numerical Algorithms for Stochastic Differential Equations
• Stochastic Lie Group Integrators
• A Theorem on the Order of Convergence of Mean-Square Approximations of Solutions of Systems of Stochastic Differential Equations
• The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
• A General Implicit Splitting for Stabilizing Numerical Simulations of Itô Stochastic Differential Equations
• First-passage-time densities for time-non-homogeneous diffusion processes
• Splitting for Dissipative Particle Dynamics
• Quasi-symplectic methods for Langevin-type equations
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Euler schemes and half-space approximation for the simulation of diffusion in a domain
• On two diffusion neuronal models with multiplicative noise: The mean first-passage time properties
• THE SPECTRAL DECOMPOSITION OF THE OPTION VALUE
• An Optimal Polynomial Approximation of Brownian Motion
• Hypoelliptic Diffusions: Filtering and Inference from Complete and Partial Observations
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes
• Geometric Numerical Integration
• On the Convergence of Ordinary Integrals to Stochastic Integrals
• On the Construction and Comparison of Difference Schemes

This page was built for publication: Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motion