Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Default Ambiguity: Finding the Best Solution to the Clearing Problem   We study financial networks with debt contracts and credit default swaps
between specific pairs of banks. Given such a financial system, we want to
decide which of the banks are in default, and how much of their liabilities can
these defaulting banks pay. There can easily be multiple different solutions to
this problem, leading to a situation of default ambiguity, and a range of
possible solutions to implement for a financial authority.
  In this paper, we study the properties of the solution space of such
financial systems, and analyze a wide range of reasonable objective functions
for selecting from the set of solutions. Examples of such objective functions
include minimizing the number of defaulting banks, minimizing the amount of
unpaid debt, maximizing the number of satisfied banks, and many others. We show
that for all of these objectives, it is NP-hard to approximate the optimal
solution to an $n^{1-\epsilon}$ factor for any $\epsilon>0$, with $n$ denoting
the number of banks. Furthermore, we show that this situation is rather
difficult to avoid from a financial regulator's perspective: the same hardness
results also hold if we apply strong restrictions on the weights of the debts,
the structure of the network, or the amount of funds that banks must possess.
However, if we restrict both the network structure and the amount of funds
simultaneously, then the solution becomes unique, and it can be found
efficiently.

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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph