Systemic Risk Assessment and Mitigation in Financial Networks Based on Optimization Modeling and Techniques

The financial crisis in 2007-2008 has inspired intensive research on the risk assessment and control in financial networks that consist of nodes representing the financial institutions and the links between them representing the interconnection among the financial institutions. Many models and techniques have been proposed to estimate the risk and identify strategy to mitigate the risk in financial networks. Among others, the clearing agent model introduced by Eisenberg and Noe (2001) and its variants have been widely adopted in risk analysis and control. A key concern in this model is the unavailability of complete information regarding the interbank liabilities and the market shock to which the asset values of the financial institutions subject. Most works in the literature assume that full information is known or use an entropy optimization approach based on the so-called Kullback-Leibler divergence to estimate the liability matrix. It has been observed, however, such an approach has led to a significant underestimation of the risk in the financial system. In this thesis, we propose to assess the systemic risk, and develop mitigation and control strategies under partial information of the underlying financial network. First, we study the vulnerability of the financial network where the asset vector subjects to market shocks. We develop a new extended sensitivity analysis to characterize the conditions under which a bank is solvent, default or bankrupted, and estimate the probability of insolvency and the probability of bankruptcy under mild conditions on the market shock and the network structure. Particularly, we show that while an increment in the social asset may not able to improve the stability of the financial system, a larger asset inequality in the system will reduce its stability. Moreover, under certain assumption on the market shock and the network structure, we show that the least stable network can be attained at some network with a monopoly node, which also has the highest probability of insolvency. The probability of bankruptcy in the network when all the nodes receive shocks is estimated. We also study the vulnerability of a well-balanced network with a monopoly node and explore the domino effect of bankruptcy in it. Numerical experiments are presented to verify the theoretical conclusions. In the second part, we study the case where only partial information regarding the liability matrix is revealed and the asset vector is fixed. We first propose two bi-level linear optimization models to identify the least and most stable network structures under which the overall repayment in the system is minimal and maximal, respectively. Then we combine several classical optimization methods with new optimization techniques to develop an integrated approach to identify the least and most stable structure in the network. Numerical experiments illustrate that the contagious risk in the identified least stable network much more significant than what underestimated in the current literature, and the system with the identified most stable network structure is the most resilient one. In the third part, we propose a new mitigation strategy based on merging and acquisitions to stabilize a financial system. For this, we first introduce some measurement to estimate the benefits of mergers in the merging process based on the extended EisenbergNoe model which takes the leverage ratio requirement and liquidation costs into account. We consider subsidized merging where the social planner provides some bail-outs to cover part of the liabilities of the insolvent bank, and develop a goal programming approach to maximize the total merger gain of the merging banks and minimize the bail-out cost for the social planner. We use major European banks linked to the adverse economic scenario used in 2016 EU-wide stress testing for demonstration. The results show that our subsidized merger policy may significantly reduce the bail-out cost compared to the generic public bail-out. Several issues are of interests for future research which is discussed in the last section.