High-order filtered schemes for time-dependent second order HJB equations

DOI10.1051/m2an/2017039zbMath1395.65012arXiv1611.04939OpenAlexW2556144876MaRDI QIDQ4579916

Olivier Bokanowski, Athena Picarelli, Christoph Reisinger

Publication date: 10 August 2018

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.04939

zbMATH Keywords

viscosity solutionshigh-order schemesmonotone schemesbackward difference formulaesecond order Hamilton-Jacobi-Bellman equations

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Second-order parabolic equations (35K10) Viscosity solutions to PDEs (35D40)

Related Items (10)

A High-Order Scheme for Image Segmentation via a Modified Level-Set Method ⋮ Executive Stock Option Exercise with Full and Partial Information on a Drift Change Point ⋮ Stability and Error Analysis for a Second-Order Fast Approximation of the Local and Nonlocal Diffusion Equations on the Real Line ⋮ Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method ⋮ A penalty scheme and policy iteration for nonlocal HJB variational inequalities with monotone nonlinearities ⋮ Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations ⋮ Some non monotone schemes for Hamilton-Jacobi-Bellman equations ⋮ Improved Accuracy of Monotone Finite Difference Schemes on Point Clouds and Regular Grids ⋮ Convergence of adaptive filtered schemes for first order evolutionary Hamilton-Jacobi equations ⋮ A Numerical Scheme for the Quantile Hedging Problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Error estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets
• Value iteration convergence of \(\varepsilon\)-monotone schemes for stationary Hamilton-Jacobi equations
• Piecewise constant policy approximations to Hamilton-Jacobi-Bellman equations
• Discontinuous Galerkin finite element methods for time-dependent Hamilton-Jacobi-Bellman equations with Cordes coefficients
• An ENO-based method for second-order equations and application to the control of dike levels
• Filtered schemes for Hamilton-Jacobi equations: a simple construction of convergent accurate difference schemes
• Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation
• A lower bound for the smallest singular value of a matrix
• On multigrid for linear complementarity problems with application to American-style options
• On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients
• Continuous-time mean-variance portfolio selection: a stochastic LQ framework
• Approximation of viscosity solutions of elliptic partial differential equations on minimal grids
• The non-locality of Markov chain approximations to two-dimensional diffusions
• Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations
• Convergent difference schemes for nonlinear parabolic equations and mean curvature motion
• Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation
• Minimal Stencils for Discretizations of Anisotropic PDEs Preserving Causality or the Maximum Principle
• Semi-Lagrangian schemes for linear and fully non-linear diffusion equations
• An Efficient Filtered Scheme for Some First Order Time-Dependent Hamilton--Jacobi Equations
• Smoothing Properties of Implicit Finite Difference Methods for a Diffusion Equation in Maximum Norm
• Some Convergence Results for Howard's Algorithm
• Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations
• User’s guide to viscosity solutions of second order partial differential equations
• Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation
• On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations
• An unconditionally monotone numerical scheme for the two-factor uncertain volatility model
• An approximation scheme for the optimal control of diffusion processes
• Some Estimates for Finite Difference Approximations
• Numerical convergence properties of option pricing PDEs with uncertain volatility
• On the Convergence of Finite Element Methods for Hamilton--Jacobi--Bellman Equations
• Convergent Filtered Schemes for the Monge--Ampère Partial Differential Equation
• Uncertain volatility and the risk-free synthesis of derivatives
• A fast algorithm for the two dimensional HJB equation of stochastic control
• Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton--Jacobi Equations and Free Boundary Problems
• Error Bounds for Monotone Approximation Schemes for Hamilton--Jacobi--Bellman Equations
• Monotone and consistent discretization of the Monge-Ampère operator
• High order numerical discretization for Hamilton-Jacobi equations on triangular meshes.

This page was built for publication: High-order filtered schemes for time-dependent second order HJB equations