Cass, for their continual guidance and constant encouragement throughout the period of the author's postgraduate studies and in the preparation of this thesis. I am very grateful to Prof. Phillip Sheung Chi Yam, former supervisor in my Master degree studies, for his dedication in guiding me during my entire postgraduate study, and for introducing me into research frontiers in mathematical finance and mean field games, including the subject of this thesis. Many ideas in this research evolved from countless discussions with him.
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