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Computer Science > Computer Science and Game Theory

arXiv:2409.18717 (cs)
[Submitted on 27 Sep 2024]

Title:Improved Hardness Results for the Clearing Problem in Financial Networks with Credit Default Swaps

Authors:Simon Dohn, Kristoffer Arnsfelt Hansen, Asger Klinkby
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Abstract:We study computational problems in financial networks of banks connected by debt contracts and credit default swaps (CDSs). A main problem is to determine \emph{clearing} payments, for instance right after some banks have been exposed to a financial shock. Previous works have shown the $\varepsilon$-approximate version of the problem to be $\mathrm{PPAD}$-complete and the exact problem $\mathrm{FIXP}$-complete. We show that $\mathrm{PPAD}$-hardness hold when $\varepsilon \approx 0.101$, improving the previously best bound significantly. Due to the fact that the clearing problem typically does not have a unique solution, or that it may not have a solution at all in the presence of default costs, several natural decision problems are also of great interest. We show two such problems to be $\exists\mathbb{R}$-complete, complementing previous $\mathrm{NP}$-hardness results for the approximate setting.
Subjects: Computer Science and Game Theory (cs.GT); Risk Management (q-fin.RM)
Cite as: arXiv:2409.18717 [cs.GT]
  (or arXiv:2409.18717v1 [cs.GT] for this version)
  https://doi.org/10.48550/arXiv.2409.18717

Submission history

From: Kristoffer Arnsfelt Hansen [view email]
[v1] Fri, 27 Sep 2024 13:02:24 UTC (25 KB)
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