We propose a simple model of inter-bank borrowing and lending where the evolution of the logmonetary reserves of N banks is described by a system of diffusion processes coupled through their drifts in such a way that stability of the system depends on the rate of inter-bank borrowing and lending. Systemic risk is characterized by a large number of banks reaching a default threshold by a given time horizon. Our model incorporates a game feature where each bank controls its rate of borrowing/lending to a central bank. The optimization reflects the desire of each bank to borrow from the central bank when its monetary reserve falls below a critical level or lend if it rises above this critical level which is chosen here as the average monetary reserve. Borrowing from or lending to the central bank is also subject to a quadratic cost at a rate which can be fixed by the regulator. We solve explicitly for Nash equilibria with finitely many players, and we show that in this model the central bank acts as a clearing house, adding liquidity to the system without affecting its systemic risk. We also study the corresponding Mean Field Game in the limit of large number of banks in the presence of a common noise.
I must acknowledge as well many friends, colleagues, students, teachers who supported, assisted, advised me on my research and who helped me writing on my dissertation. Thanks also to my department who gave me the great financial support during my studies and provided these great courses of financial mathematics and statistics. A special thanks to my family. Words cannot express how grateful I am to my mother and father for your support and sacrifices. Your encouragement and prayer were what sustained me thus far.
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