Optimal monitoring and mitigation of systemic risk in lending networks

This thesis proposes optimal policies to manage systemic risk in financial networks. Given a one-period borrower-lender network in which all debts are due at the same time and have the same seniority, we address the problem of allocating a fixed amount of cash among the nodes to minimize the weighted sum of unpaid liabilities. Assuming all the loan amounts and cash flows are fixed and that there are no bankruptcy costs, we show that this problem is equivalent to a linear program. We develop a duality-based distributed algorithm to solve it which is useful for applications where it is desirable to avoid centralized data gathering and computation. Since some applications require forecasting and planning for a wide variety of different contingencies, we introduce a stochastic model for the institutions operating cash and consider the problem of minimizing the expectation of the weighted sum of unpaid liabilities. We show that this problem is a two-stage stochastic linear program and develop an online learning algorithm based on stochastic gradient descent to solve it. We consider a number of further extensions of our deterministic scenario by incorporating various additional features of real-world lending networks into our model. For example, we show that if the defaulting nodes do not pay anything, then the optimal cash injection allocation problem is a mixed-integer linear program. In addition, we develop and evaluate two heuristic algorithms to allocate the cash injection amount so as to minimize the number of nodes in default. Our results provide algorithmic tools to help financial institutions, banking supervisory authorities, regulatory agencies, and clearing houses in monitoring and mitigating systemic risk in financial networks