On the equality of solutions of max–min and min–max systems of variational inequalities with interconnected bilateral obstacles

Boualem Djehiche, Said Hamadène, Marie Amélie Morlais, Xuzhe Zhao

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we deal with the solutions of systems of PDEs with bilateral interconnected obstacles of min–max and max–min types. These systems arise naturally in stochastic switching zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min–max and max–min systems coincide. Then, this common viscosity solution is related to a multi-dimensional doubly reflected BSDE with bilateral interconnected obstacles. Finally, its relationship with the values of a zero-sum switching game is studied.

Original languageEnglish (US)
Pages (from-to)148-175
Number of pages28
JournalJournal of Mathematical Analysis and Applications
Volume452
Issue number1
DOIs
StatePublished - Aug 1 2017

Keywords

  • Hamilton–Jacobi–Bellman–Isaacs equation
  • PDEs with obstacles
  • Reflected backward stochastic differential equation
  • Switching zero-sum game

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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