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/272918>.

@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; verification theorem},
language = {eng},
number = {3},
pages = {749-760},
publisher = {EDP-Sciences},
title = {Stochastic differential games involving impulse controls},
url = {http://eudml.org/doc/272918},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Zhang, Feng
TI - Stochastic differential games involving impulse controls
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
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; verification theorem
UR - http://eudml.org/doc/272918
ER -

References

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  2. [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. Zbl1157.93040MR2373477
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  8. [8] R. Korn, Some applications of impulse control in mathematical finance. Math. Meth. Oper. Res.50 (1999) 493–518. Zbl0942.91048MR1731297
  9. [9] B. Øksendal and A. Sulem, Optimal stochastic impulse control with delayed reaction. Appl. Math. Optim.58 (2008) 243–255. Zbl1161.93029MR2439661
  10. [10] L.C.G. Rogers and D. Williams, Diffusions, Markov processes, and martingales. John Wiley & Sons, New York (1987). Zbl0826.60002MR921238
  11. [11] A.J. Shaiju and S. Dharmatti, Differential games with continuous, switching and impulse controls. Nonlinear Anal.63 (2005) 23–41. Zbl1132.91356MR2167312
  12. [12] J. Yong, Systems governed by ordinary differential equations with continuous, switching and impulse controls. Appl. Math. Optim.20 (1989) 223–235. Zbl0691.49031MR1004708
  13. [13] J. Yong, Zero-sum differential games involving impulse controls. Appl. Math. Optim.29 (1994) 243–261. Zbl0808.90142MR1264011

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