Multi-dimensional BSDE with oblique reflection and optimal switching

DOI10.1007/s00440-009-0202-1zbMath1188.60029arXiv0706.4365OpenAlexW2592216957MaRDI QIDQ2380763

Ying Hu, Shanjian Tang

Publication date: 12 April 2010

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.4365

zbMATH Keywords

viscosity solutiona priori estimatespenalization methodmonotone convergenceoptimal switching problemmulti-dimensional backward stochastic differential equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Optimal stochastic control (93E20)

Related Items (75)

Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles of non-local type ⋮ The finite horizon optimal multi-modes switching problem: the viscosity solution approach ⋮ Existence, uniqueness and regularity of solutions to systems of nonlocal obstacle problems related to optimal switching ⋮ Optimal switching at Poisson random intervention times ⋮ Optimal switching problem and related system of BSDEs with left-Lipschitz coefficients and mixed reflections ⋮ Swing Options Valuation: A BSDE with Constrained Jumps Approach ⋮ An existence theorem for multidimensional BSDEs with mixed reflections ⋮ Sequential systems of reflected backward stochastic differential equations with application to impulse control ⋮ Systems of fully nonlinear parabolic obstacle problems with Neumann boundary conditions ⋮ Reflected BSDEs in non-convex domains ⋮ Viscosity solutions of systems of PDEs with interconnected obstacles and switching problem ⋮ On the equality of solutions of max-min and min-max systems of variational inequalities with interconnected bilateral obstacles ⋮ Management strategies for run-of-river hydropower plants: an optimal switching approach ⋮ Backward doubly SDEs and semilinear stochastic PDEs in a convex domain ⋮ Existence, uniqueness and approximation for \(L^p\) solutions of reflected BSDEs with generators of one-sided Osgood type ⋮ Infinite horizon impulse control problem with jumps and continuous switching costs ⋮ Obstacle problem for evolution equations involving measure data and operator corresponding to semi-Dirichlet form ⋮ On a switching control problem with càdlàg costs ⋮ Optimal switching problem and system of reflected multi-dimensional FBSDEs with random terminal time ⋮ Systems of reflected BSDEs with interconnected bilateral obstacles: existence, uniqueness and applications ⋮ Systems of integro-PDEs with interconnected obstacles and multi-modes switching problem driven by Lévy process ⋮ Systems of fully nonlinear degenerate elliptic obstacle problems with Dirichlet boundary conditions ⋮ Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection ⋮ Systems of quasi-variational inequalities related to the switching problem ⋮ Infinite horizon multi-dimensional BSDE with oblique reflection and switching problem ⋮ Probabilistic representation of viscosity solutions to quasi-variational inequalities with non-local drivers ⋮ Viscosity solution of system of integro-partial differential equations with interconnected obstacles of non-local type without monotonicity conditions ⋮ Zero-sum stochastic differential games of impulse versus continuous control by FBSDEs ⋮ Multi-dimensional BSDEs with mean reflection ⋮ Reflected backward stochastic difference equations and optimal stopping problems under \(g\)-expectation ⋮ Viscosity solutions of system of PDEs with interconnected obstacles and nonlinear Neumann boundary conditions ⋮ Anticipated backward stochastic variational inequalities with generalized reflection ⋮ Numerical methods for backward stochastic differential equations: a survey ⋮ Principal-agent problem with multiple principals ⋮ System of nonlinear second-order parabolic partial differential equations with interconnected obstacles and oblique derivative boundary conditions on non-smooth time-dependent domains ⋮ Time discretization and quantization methods for optimal multiple switching problem ⋮ Discrete-time approximation of multidimensional BSDEs with oblique reflections ⋮ Systems of variational inequalities for non-local operators related to optimal switching problems: existence and uniqueness ⋮ Reflected BSDEs with jumps in time-dependent convex càdlàg domains ⋮ Infection time in multistable gene networks. A backward stochastic variational inequality with nonconvex switch-dependent reflection approach ⋮ Liquidity risk and optimal dividend/investment strategies ⋮ A Brownian optimal switching problem under incomplete information ⋮ BSDEs with mean reflection ⋮ Quadratic BSDEs with mean reflection ⋮ BSDE representations for optimal switching problems with controlled volatility ⋮ Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems ⋮ \(L^1\) solutions of non-reflected BSDEs and reflected BSDEs with one and two continuous barriers under general assumptions ⋮ Probabilistic representation and approximation for coupled systems of variational inequalities ⋮ Obliquely reflected backward stochastic differential equations ⋮ Comparison theorem for diagonally quadratic BSDEs ⋮ A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time ⋮ Stochastic hybrid differential games and match race problems ⋮ A two-scale scheme for finite horizon switching problems with delays ⋮ Optimal switching under a hybrid diffusion model and applications to stock trading ⋮ Forward-backward stochastic differential equation with subdifferential operator and associated variational inequality ⋮ A full balance sheet two-mode optimal switching problem ⋮ Existence, uniqueness and stability of \(L^1\) solutions for multidimensional backward stochastic differential equations with generators of one-sided Osgood type ⋮ On the finite horizon optimal switching problem with random lag ⋮ Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type ⋮ Reflected BSDE of Wiener-Poisson type in time-dependent domains ⋮ A balance sheet optimal multi-modes switching problem ⋮ Robust Feedback Switching Control: Dynamic Programming and Viscosity Solutions ⋮ Optimal switching problems with an infinite set of modes: an approach by randomization and constrained backward SDEs ⋮ Systems of BSDES with oblique reflection and related optimal switching problems ⋮ Switching problems with controlled randomisation and associated obliquely reflected BSDEs ⋮ \(\mathbb{L}^2\)-solutions for reflected BSDEs with jumps under monotonicity and general growth conditions: a penalization method ⋮ Infinite-Horizon Optimal Switching Regions for a Pair-Trading Strategy with Quadratic Risk Aversion Considering Simultaneous Multiple Switchings: A Viscosity Solution Approach ⋮ Robust classical-impulse stochastic control problems in an infinite horizon ⋮ A finite horizon optimal switching problem with memory and application to controlled SDDEs ⋮ Stochastic Control Representations for Penalized Backward Stochastic Differential Equations ⋮ Quadratic mean-field reflected BSDEs ⋮ Multivalued backward stochastic differential equations with oblique subgradients ⋮ Ergodicity of Robust Switching Control and Nonlinear System of Quasi-Variational Inequalities ⋮ Switching game of backward stochastic differential equations and associated system of obliquely reflected backward stochastic differential equations ⋮ Reflected stochastic differential equations driven by \(G\)-Brownian motion with nonlinear resistance

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adapted solution of a backward stochastic differential equation
• Reflected backward stochastic differential equations in an orthant
• Valuation of power plants by utility indifference and numerical computation
• Reflected solutions of backward SDE's, and related obstacle problems for PDE's
• On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case.
• SDEs with oblique reflection on nonsmooth domains
• On the comparison theorem for multidimensional BSDEs
• Backward stochastic differential equations and integral-partial differential equations
• A Finite Horizon Optimal Multiple Switching Problem
• Pricing Asset Scheduling Flexibility using Optimal Switching
• Stochastic differential equations with reflecting boundary conditions
• User’s guide to viscosity solutions of second order partial differential equations
• Finite horizon stochastic optimal switching and impulse controls with a viscosity solution approach
• Equations différentielles stochastiques rétrogrades réfléchies dans un convexe
• On the Starting and Stopping Problem: Application in Reversible Investments

This page was built for publication: Multi-dimensional BSDE with oblique reflection and optimal switching