Abstract
Agents in financial networks can simultaneously be both creditors and debtors, creating the possibility that a default may cause a subsequent default cascade. Resolution of unpayable debts in these situations will have a distributional impact. Using a relative entropy-based measure of the distributional impact of the subsequent default resolution process, it is argued that minimum mutual information estimation of unknown cells in the matrix of funds originally owed by the network participants to each other does not introduce systematic biases when estimating that impact.
Highlights
The standard representation of a payments network starts with a snapshot of gross liabilities owed by each agent to each other agent, in the form of a matrix L L= L21 L N1 L12 L N2 L1NL2N in which Lij is an amount that agent i owes to agent j
In order to provide evidence based on comparisons to matrices with identical row and column totals, each matrix produced by permutation is considered as another matrix (1) and paired with the minimum mutual information matrix produced from its row and column totals, considered as matrix (7)
The minimum mutual problems information estimator has been used as an objective function inmatrices, constrained constrained minimization for estimating unknown cells in interagent liability and constrained minimization problems for estimating unknown cells in interagent liability matrices, and minimization problems for estimating unknown in interagent liability matrices, and analogous analogous matrices matrices arising in the the social social sciences.cells
Summary
The standard representation of a payments network starts with a snapshot of gross liabilities owed by each agent (bank, firm, trader, etc.) to each other agent, in the form of a matrix L. Entropy 2018, 20, 369 available from its a3 = 50 in assets to pay its l3 = 50 in total liabilities, and will have to default on some payments if it does not receive payment from the defaulting agent #2. Elimam et al [2] and Eisenberg and Noe [3], the literature has focused on the following default resolution rule: after any default cascade has ended, an agent that can pay only θ% of its total liabilities must pay exactly θ% of the funds owed to each of its creditors. This raises the issue of whether or not this estimator of unknown cells systematically biases estimation of the distributional impact index.
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