# Stochastic differential games involving impulse controls*

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

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

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topZhang, 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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- B. Øksendal and A. Sulem, Optimal stochastic impulse control with delayed reaction. Appl. Math. Optim.58 (2008) 243–255. Zbl1161.93029
- L.C.G. Rogers and D. Williams, Diffusions, Markov processes, and martingales. John Wiley & Sons, New York (1987). Zbl0627.60001
- A.J. Shaiju and S. Dharmatti, Differential games with continuous, switching and impulse controls. Nonlinear Anal.63 (2005) 23–41. Zbl1132.91356
- J. Yong, Systems governed by ordinary differential equations with continuous, switching and impulse controls. Appl. Math. Optim.20 (1989) 223–235. Zbl0691.49031
- J. Yong, Zero-sum differential games involving impulse controls. Appl. Math. Optim.29 (1994) 243–261. Zbl0808.90142

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