
The Computational Complexity of Clearing Financial Networks with Credit Default Swaps
We consider the problem of clearing a system of interconnected banks. Pr...
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Default Ambiguity: Finding the Best Solution to the Clearing Problem
We study financial networks with debt contracts and credit default swaps...
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CDS Rate Construction Methods by Machine Learning Techniques
Regulators require financial institutions to estimate counterparty defau...
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NetworkAware Strategies in Financial Systems
We study the incentives of banks in a financial network, where the netwo...
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Sequential Defaulting in Financial Networks
We consider financial networks, where banks are connected by contracts s...
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Credit Freezes, Equilibrium Multiplicity, and Optimal Bailouts in Financial Networks
We analyze how interdependencies between organizations in financial netw...
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Allocating Stimulus Checks in Times of Crisis
We study the problem of allocating bailouts (stimulus, subsidy allocatio...
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Strong Approximations and Irrationality in Financial Networks with Financial Derivatives
Financial networks model a set of financial institutions (firms) interconnected by obligations. Recent work has introduced to this model a class of obligations called credit default swaps, a certain kind of financial derivatives. The main computational challenge for such systems is known as the clearing problem, which is to determine which firms are in default and to compute their exposure to systemic risk, technically known as their recovery rates. It is known that the recovery rates form the set of fixed points of a simple function, and that these fixed points can be irrational. Furthermore, Schuldenzucker et al. (2016) have shown that finding a weakly (or "almost") approximate (rational) fixed point is PPADcomplete. In light of the above, we further study the clearing problem from the point of view of irrationality and approximation strength. Firstly, as weakly approximate solutions are hard to justify for financial institutions, we study the complexity of finding a strongly (or "near") approximate solution, and show FIXPcompleteness. Secondly, we study the structural properties required for irrationality, and we give necessary conditions for irrational solutions to emerge: The presence of certain types of cycles in a financial network forces the recovery rates to take the form of roots of second or higherdegree polynomials. In the absence of a large subclass of such cycles, we study the complexity of finding an exact fixed point, which we show to be a problem close to, albeit outside of, PPAD.
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