Said Hamadene

On the Existence of a Value of Zero-sum Switching Games

with General Switching Costs

In this talk we discuss the problem of existence of a value for the zero-sum switching game in the Markovian framework. The switching costs are not constant and can depend on time and the diffusion process as well. We show that the game has a value. The techniques combine the notion of backward stochastic differential equation and viscosity solutions of systems of PDEs. This is a joint work with Marcus Olofsson, University of Uppsala, Sweden.

References

Djehiche, B., Hamadene, S., Morlais, M.-A. (2015). Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles. Funkcialaj Ekvacioj 58, pp. 135-175.

Djehiche, B., Hamadene, S., Morlais, M.-A., Zhao, X. (2017). On the equality of solutions of max–min and min–max systems of variational inequalities with interconnected bilateral obstacles. Journal of Mathematical Analysis and Applications 452, pp. 148-175.

Tang S., Hou, S.-H. (2007) Switching games of stochastic differential systems. SIAM Journal on Control and Optimization 46, pp. 900-929.

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