Representation formulas for solutions of Isaacs integro-PDE

Shigeaki Koike, Andrzej Świȩch

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We prove sub-and super-optimality inequalities of dynamic programming for viscosity solutions of Isaacs integro-PDE associated with two-player, zero-sum stochastic differential game driven by a Lévy-type noise. This implies that the lower and upper value functions of the game satisfy the dynamic programming principle and that they are the unique viscosity solutions of the lower and upper Isaacs integro-PDE. We show how to regularize viscosity sub-and super-solutions of Isaacs equations to smooth sub-and supersolutions of slightly perturbed equations.

Original languageEnglish
Pages (from-to)1473-1502
Number of pages30
JournalIndiana University Mathematics Journal
Volume62
Issue number5
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Integro-PDE
  • Isaacs equation
  • Lévy process
  • Stochastic differential equation
  • Stochastic differential game
  • Viscosity solutions

ASJC Scopus subject areas

  • Mathematics(all)

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