Advances in Applied Probability

Nash equilibrium payoffs for stochastic differential games with two reflecting barriers

Qian Lin

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper we study Nash equilibrium payoffs for nonzero-sum stochastic differential games with two reflecting barriers. We obtain an existence and a characterization of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations with two reflecting barriers.

Article information

Source
Adv. in Appl. Probab., Volume 47, Number 2 (2015), 355-377.

Dates
First available in Project Euclid: 25 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.aap/1435236979

Digital Object Identifier
doi:10.1239/aap/1435236979

Mathematical Reviews number (MathSciNet)
MR3360381

Zentralblatt MATH identifier
1329.49070

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 91A15: Stochastic games 91A23: Differential games [See also 49N70]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 90C39: Dynamic programming [See also 49L20]

Keywords
Nash equilibrium payoff stochastic differential game backward stochastic differential equation

Citation

Lin, Qian. Nash equilibrium payoffs for stochastic differential games with two reflecting barriers. Adv. in Appl. Probab. 47 (2015), no. 2, 355--377. doi:10.1239/aap/1435236979. https://projecteuclid.org/euclid.aap/1435236979


Export citation

References

  • Barles, G., Buckdahn, R. and Pardoux, E. (1997). Backward stochastic differential equations and integral-partial differential equations. Stoch. Reports 60, 57–83.
  • Buckdahn, R., Cardaliaguet, P. and Quincampoix, M. (2011). Some recent aspects of differential game theory. Dyn. Games Appl. 1, 74–114.
  • Buckdahn, R., Cardaliaguet, P. and Rainer, C. (2004). Nash equilibrium payoffs for nonzero-sum stochastic differential games. SIAM J. Control Optimization 43, 624–642.
  • Buckdahn, R. and Li, J. (2008). Stochastic differential games and viscosity solutions of Hamilton–Jacobi–Bellman–Isaacs equations. SIAM J. Control Optimization 47, 444–475.
  • Buckdahn, R. and Li, J. (2009). Probabilistic interpretation for systems of Isaacs equations with two reflecting barriers. Nonlinear Differential Equations Appl. 16, 381–420.
  • Cvitanić, J. and Karatzas, I. (1996). Backward stochastic differential equations with reflection and Dynkin games. Ann. Prob. 24, 2024–2056.
  • Duffie, D. and Epstein, L. G. (1992). Stochastic differential utility. Econometrica 60, 353–394.
  • El Karoui, N., Peng, S. and Quenez, M. C. (1997). Backward stochastic differential equation in finance. Math. Finance 7, 1–71.
  • Fleming, W. H. and Souganidis, P. E. (1989). On the existence of value functions of two-player, zero-sum stochastic differential games. Indiana Univ. Math. J. 38, 293–314.
  • Hamadène, S. and Hassani, M. (2005). BSDEs with two reflecting barriers: the general result. Prob. Theory Relat. Fields 132, 237–264.
  • Lin, Q. (2012). A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals. Stoch. Process. Appl. 122, 357–385.
  • Lin, Q. (2013). Nash equilibrium payoffs for stochastic differential games with reflection. ESAIM Control Optimization Calc. Var. 19, 1189–1208.
  • Pardoux, É. and Peng, S. G. (1990). Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14, 55–61.
  • Peng, S. (1997). Backward stochastic differential equations–-stochastic optimization theory and viscosity solutions of HJB equations. In Topics in Stochastic Analysis, eds J. Yan et al,, Science Press, Beijing, pp. 85–138.
  • Pham, T. and Zhang, J. (2013). Some norm estimates for semimartingales. Electron. J. Prob. 18, 1–25.