Abstract
We consider a large class of stochastic differential games for several players. The class includes Nash differential games as well as Stackelberg differential games. A mix is possible. We prove existence of feedback strategies under general conditions. The limitations concern the functional in which the state and the controls appear separately. This is also true for the state equations. The controls appear in a quadratic form for the payoff and linearly in the state equation. The most serious restriction is the dimension of the state equation, which cannot exceed 2.
The reason comes from PDE (partial differential equations) techniques used in studying the system of Bellman equations obtained by Dynamic Programming arguments. In our previous work, there is not such a restriction, but there are serious restrictions on the structure of the Hamiltonians, which are violated in the applications dealt with in this article.
About the speaker
Prof Alain Bensoussan is an internationally acclaimed scholar in the field of stochastic control, inventory management and risk and decision analysis. In particular, he introduced impulse control in the context of inventory management. The concepts and methods developed in this context have since been widely used in many domains of management science and operations research. Before joining Hong Kong Polytechnic University in
2009 as Chair Professor of Risk and Decision Analysis in the Faculty of Business, Prof Bensoussan was already involved in the mutual insurance activities of the Faculty of Business, using impulse control methodology.
During his career in Europe, Professor Bensoussan had held many important responsibilities in research establishments. In particular, he was Chairman of the European Space Agency (ESA) Council, President of the Centre National d'Etudes Spatiales (CNES) and President of the Institut National de Recherche en Informatique et en Automatique (INRIA).
Prof Bensoussan is a member of French Academy of Sciences, French Academy of Technology, International Academy of Astronautics and Academia Europaea and Fellow of IEEE. He received the Von Humboldt Prize in 1984 and the distinctions of Commandeur de l'Ordre National du M'erite in 2000 and Officier de la L'egion d'Honneur in 2003.
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