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stochastic differentialgame

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Stochastic differential games involving impulse controls *
Feng Zhang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 3 / July 2011

Published online by Cambridge University Press:

23 April 2010, pp. 749-760

Print publication:

July 2011
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A zero-sum stochastic differential gameproblem on infinite horizon with continuous and impulse controls isstudied. We obtain the existence of the value of the game andcharacterize it as the unique viscosity solution of the associatedsystem of quasi-variational inequalities. We also obtain averification theorem which provides an optimal strategy of the game.