Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles

Boualem Djehiche; Said Hamadène; Marie Amelie Morlais

doi:10.1619/fesi.58.135

Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles

Boualem Djehiche, Said Hamadène, Marie Amelie Morlais

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward SDEs, we construct a continuous viscosity solution of polynomial growth. Moreover, we establish a comparison result which in turn yields uniqueness of the solution.

Original language	English (US)
Pages (from-to)	135-175
Number of pages	41
Journal	Funkcialaj Ekvacioj
Volume	58
Issue number	1
DOIs	https://doi.org/10.1619/fesi.58.135
State	Published - Apr 9 2015

Keywords

Backward stochastic differential equation
Bellman-Isaacs equation
Oblique reflection
Penalization
Perron’s method
Switching games
Variational inequalities

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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year = "2015",

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AU - Hamadène, Said

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AB - We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward SDEs, we construct a continuous viscosity solution of polynomial growth. Moreover, we establish a comparison result which in turn yields uniqueness of the solution.

KW - Backward stochastic differential equation

KW - Bellman-Isaacs equation

KW - Oblique reflection

KW - Penalization

KW - Perron’s method

KW - Switching games

KW - Variational inequalities

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Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles

Abstract

Keywords

ASJC Scopus subject areas

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