Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance
From MaRDI portal
Publication:379049
DOI10.3934/dcdsb.2013.18.2083zbMath1279.60068arXiv1204.1647OpenAlexW2022278178MaRDI QIDQ379049
Xuerong Mao, Desmond J. Higham, Lukasz Szpruch
Publication date: 12 November 2013
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1204.1647
stabilitystrong convergenceMilstein schemenonnegativityimplicit schemes stochastic differential equation
Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Numerical solutions to equations with nonlinear operators (65J15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)
Related Items (44)
Analysis of non-negativity and convergence of solution of the balanced implicit method for the delay Cox-Ingersoll-Ross model ⋮ Split-step theta Milstein methods for SDEs with non-globally Lipschitz diffusion coefficients ⋮ Approximation of Non-Lipschitz SDEs by Picard Iterations ⋮ Construction of positivity preserving numerical method for jump-diffusion option pricing models ⋮ Stability analysis of stochastic delay differential equations with Markovian switching driven by Lévy noise ⋮ Stationary distribution of the Milstein scheme for stochastic differential delay equations with first-order convergence ⋮ Double-implicit and split two-step Milstein schemes for stochastic differential equations ⋮ Convergence and stability of the Milstein scheme for stochastic differential equations with piecewise continuous arguments ⋮ Convergence and stability of two classes of theta-Milstein schemes for stochastic differential equations ⋮ Strong convergence of an adaptive time-stepping Milstein method for SDEs with monotone coefficients ⋮ Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients ⋮ Strong convergence rate of implicit Euler scheme to a CIR model with delay ⋮ $V$-integrability, asymptotic stability and comparison property of explicit numerical schemes for non-linear SDEs ⋮ Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients ⋮ Positivity-preserving truncated Euler-Maruyama method for generalised Ait-Sahalia-type interest model ⋮ Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations ⋮ Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations ⋮ Construction of positivity-preserving numerical method for stochastic SIVS epidemic model ⋮ Construction of positivity preserving numerical schemes for some multidimensional stochastic differential equations ⋮ Construction of positivity preserving numerical method for stochastic age-dependent population equations ⋮ Truncated Milstein method for non-autonomous stochastic differential equations and its modification ⋮ A transformed jump-adapted backward Euler method for jump-extended CIR and CEV models ⋮ Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs ⋮ Numerical analysis of the balanced implicit method for stochastic age-dependent capital system with Poisson jumps ⋮ Invariant measures of the Milstein method for stochastic differential equations with commutative noise ⋮ Implicit Milstein method for stochastic differential equations via the Wong-Zakai approximation ⋮ The positive numerical solution for stochastic age-dependent capital system based on explicit-implicit algorithm ⋮ Convergence and non-negativity preserving of the solution of balanced method for the delay CIR model with jump ⋮ Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations ⋮ Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations ⋮ Convergence, non-negativity and stability of a new lobatto IIIC-Milstein method for a pricing option approach based on stochastic volatility model ⋮ First order strong approximations of scalar SDEs defined in a domain ⋮ High‐order split‐step theta methods for non‐autonomous stochastic differential equations with non‐globally Lipschitz continuous coefficients ⋮ Strong convergence of a GBM based tamed integrator for SDEs and an adaptive implementation ⋮ Explicit Milstein schemes with truncation for nonlinear stochastic differential equations: convergence and its rate ⋮ Positivity preserving stochastic \(\theta\)-methods for selected SDEs ⋮ A two-parameter Milstein method for stochastic Volterra integral equations ⋮ Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion ⋮ Strong and weak convergence rates of logarithmic transformed truncated EM methods for SDEs with positive solutions ⋮ A positivity-preserving numerical algorithm for stochastic age-dependent population system with Lévy noise in a polluted environment ⋮ Positivity-preserving numerical schemes for stochastic differential equations ⋮ Two-step Milstein schemes for stochastic differential equations ⋮ Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes ⋮ Study on split-step Rosenbrock type method for stiff stochastic differential systems
This page was built for publication: Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance
