Representation formulas for solutions of Isaacs integro-PDE

Shigeaki Koike, Andrzej Świȩch

Research output: Contribution to journalArticle

6 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 Jan 1
Externally publishedYes

Fingerprint

Sub- and Supersolutions
Representation Formula
Viscosity Solutions
Lower and Upper Functions
Dynamic Programming Principle
Isaacs Equation
Stochastic Differential Games
Zero-sum
Value Function
Dynamic Programming
Optimality
Viscosity
Game
Imply

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Representation formulas for solutions of Isaacs integro-PDE. / Koike, Shigeaki; Świȩch, Andrzej.

In: Indiana University Mathematics Journal, Vol. 62, No. 5, 01.01.2013, p. 1473-1502.

Research output: Contribution to journalArticle

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