Conclusion
In this paper, we study the risk contagion problem and characterize analytically the effect of the liquidation mechanism on the total wealth of financial networks. We formulate contagion reduction as a performance optimization problem with nonlinear constraints. We apply the direct-comparison based approach to solve this problem. In this approach, we derive the performance difference formula which clearly shows the details of the differences of any two liquidation schemes, and we derive the directional derivatives of the performance measures in the policy space. Some optimality properties are obtained. Furthermore, we develop a policy iteration–gradient combined algorithm for the optimal liquidation scheme. Finally, we provide some examples to illustrate the efficiency of our algorithm for reducing the system’s loss and the number of default banks. Compared with the pro rata scheme, our proposed optimal liquidation scheme reduces the system’s total debts and save banks from defaulting. This provides a new direction for curbing the contagion among financial institutes for the government and central bank to consider during financial crisis. The direct-comparison based approach to performance optimization was first developed for discrete event dynamic systems, and has been applied to many theoretical as well as practical problems. In this paper, we find that surprisingly the performance difference formula for the risk contagion problem looks similar to that in MDPs. Our research indicates that this approach can also be applied to static problems such as the risk contagion problem. In addition, since for some other problems, ‘‘fairness’’ is not an essence, our results of this paper can be extended to these contexts, such as power grids systems, logistics systems, and some other network systems.
