Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type

DOI10.1007/s10231-013-0325-yzbMath1302.35226OpenAlexW2051128094MaRDI QIDQ741307

Kaj Nyström, Niklas L. P. Lundström, Marcus Olofsson

Publication date: 11 September 2014

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-013-0325-y

zbMATH Keywords

sub- and supersolutionsobstacle problemKolmogorov equationreflected backward stochastic differential equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) PDEs with randomness, stochastic partial differential equations (35R60) Existence theories for optimal control problems involving partial differential equations (49J20) Ultraparabolic equations, pseudoparabolic equations, etc. (35K70) Viscosity solutions to PDEs (35D40) Comparison principles in context of PDEs (35B51) Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators (35K87)

Related Items (15)

Existence, uniqueness and regularity of solutions to systems of nonlocal obstacle problems related to optimal switching ⋮ System of variational inequalities with interconnected obstacles ⋮ Systems of fully nonlinear parabolic obstacle problems with Neumann boundary conditions ⋮ 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 ⋮ Obstacle problem for evolution equations involving measure data and operator corresponding to semi-Dirichlet form ⋮ Systems of fully nonlinear degenerate elliptic obstacle problems with Dirichlet boundary conditions ⋮ Systems of quasi-variational inequalities related to the switching problem ⋮ Systems of variational inequalities for non-local operators related to optimal switching problems: existence and uniqueness ⋮ A Brownian optimal switching problem under incomplete information ⋮ A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time ⋮ A full balance sheet two-mode optimal switching problem ⋮ Error Estimates of Penalty Schemes for Quasi-Variational Inequalities Arising from Impulse Control Problems ⋮ Optimal switching problems with an infinite set of modes: an approach by randomization and constrained backward SDEs ⋮ Finite-Horizon Optimal Multiple Switching with Signed Switching Costs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Viscosity solutions of systems of PDEs with interconnected obstacles and switching problem
• Adapted solution of a backward stochastic differential equation
• Viscosity solutions for a system of integro-PDEs and connections to optimal switching and control of jump-diffusion processes
• Regularity near the initial state in the obstacle problem for a class of hypoelliptic ultraparabolic operators
• The finite horizon optimal multi-modes switching problem: the viscosity solution approach
• Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form
• Switching problem and related system of reflected backward SDEs
• Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options
• A PDE approach to regularity of solutions to finite horizon optimal switching problems
• Reflected solutions of backward SDE's, and related obstacle problems for PDE's
• Multi-dimensional BSDE with oblique reflection and optimal switching
• Hypoelliptic second order differential equations
• Optimal Switching over Multiple Regimes
• A Finite Horizon Optimal Multiple Switching Problem
• User’s guide to viscosity solutions of second order partial differential equations
• ON A FINITE HORIZON STARTING AND STOPPING PROBLEM WITH RISK OF ABANDONMENT

This page was built for publication: Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type