Stochastic differential games in a non-markovian setting

Erhan Bayraktar, H. Vincent Poor

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Stochastic differential games are considered in a non-Markovian setting. Typically, in stochastic differential games the modulating process of the diffusion equation describing the state flow is taken to be Markovian. Then Nash equilibria or other types of solutions such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method is not applicable. To examine the non-Markovian case, this paper considers the situation in which the modulating process is a fractional Brownian motion. Fractional noise calculus is used for such models to find the Nash equilibria explicitly. Although fractional Brownian motion is taken as the modulating process because of its versatility in modeling in the fields of finance and networks, the approach in this paper has the merit of being applicable to more general Gaussian stochastic differential games with only slight conceptual modifications. This work has applications in finance to stock price modeling which incorporates the effect of institutional investors, and to stochastic differential portfolio games in markets in which the stock prices follow diffusions modulated with fractional Brownian motion.

Original languageEnglish (US)
Pages (from-to)1737-1756
Number of pages20
JournalSIAM Journal on Control and Optimization
Volume43
Issue number5
DOIs
StatePublished - Nov 14 2005

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Keywords

  • Fractional Brownian motion
  • Fractional noise theory
  • Non-Markovian games
  • Stochastic differential games

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