Stochastic differential games involving impulse controls*

Feng Zhang

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 3, page 749-760
  • ISSN: 1292-8119

Abstract

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A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.

How to cite

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Zhang, Feng. "Stochastic differential games involving impulse controls*." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 749-760. <http://eudml.org/doc/221926>.

@article{Zhang2011,
abstract = { A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game. },
author = {Zhang, Feng},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Stochastic differential game; impulse control; quasi-variational inequalities; viscosity solution; stochastic differential games; quasi-variational inequality; Elliott-Kalton value; viscosity solution; verification theorem},
language = {eng},
month = {8},
number = {3},
pages = {749-760},
publisher = {EDP Sciences},
title = {Stochastic differential games involving impulse controls*},
url = {http://eudml.org/doc/221926},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Zhang, Feng
TI - Stochastic differential games involving impulse controls*
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2011/8//
PB - EDP Sciences
VL - 17
IS - 3
SP - 749
EP - 760
AB - A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.
LA - eng
KW - Stochastic differential game; impulse control; quasi-variational inequalities; viscosity solution; stochastic differential games; quasi-variational inequality; Elliott-Kalton value; viscosity solution; verification theorem
UR - http://eudml.org/doc/221926
ER -

References

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  2. R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions of Hamiltonian-Jacobi-Bellman-Isaacs equations. SIAM J. Control Optim.47 (2008) 444–475.  Zbl1157.93040
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  7. W.H. Fleming and P.E. Souganidis, On the existence of value functions of two-player, zero-sum stochastic differential games. Indiana Univ. Math. J.38 (1989) 293–314.  Zbl0686.90049
  8. R. Korn, Some applications of impulse control in mathematical finance. Math. Meth. Oper. Res.50 (1999) 493–518.  Zbl0942.91048
  9. B. Øksendal and A. Sulem, Optimal stochastic impulse control with delayed reaction. Appl. Math. Optim.58 (2008) 243–255.  Zbl1161.93029
  10. L.C.G. Rogers and D. Williams, Diffusions, Markov processes, and martingales. John Wiley & Sons, New York (1987).  Zbl0627.60001
  11. A.J. Shaiju and S. Dharmatti, Differential games with continuous, switching and impulse controls. Nonlinear Anal.63 (2005) 23–41.  Zbl1132.91356
  12. J. Yong, Systems governed by ordinary differential equations with continuous, switching and impulse controls. Appl. Math. Optim.20 (1989) 223–235.  Zbl0691.49031
  13. J. Yong, Zero-sum differential games involving impulse controls. Appl. Math. Optim.29 (1994) 243–261.  Zbl0808.90142

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