@article{2b25338fb0054cfc86e1c3b8bdee0818,
title = "Trading networks and hodge theory",
abstract = "The problem of analyzing interconnectedness is one of today{\textquoteright}s premier challenges in understanding systemic risk. Connections can both stabilize networks and provide pathways for contagion. The central problem in such networks is establishing global behavior from local interactions. Jiang-Lim-Yao-Ye (Jiang et al 2011 Mathematical Programming 127 1 203–244) recently introduced the use of the Hodge decomposition (see Lim 2020 SIAM Review 62 685–715 for a review), a fundamental tool from algebraic geometry, to construct global rankings from local interactions (see Barbarossa et al 2018 (2018 IEEE Data Science Workshop (DSW), IEEE) pp 51–5; Haruna and Fujiki 2016 Frontiers in Neural Circuits 10 77; Jia et al 2019 (Proc. of the XXV ACM SIGKDD International Conf. on Knowledge Discovery & Data Mining, pp 761–71 for other applications). We apply this to a study of financial networks, starting from the Eisenberg-Noe (Eisenberg and Noe 2001 Management Science 47 236–249) setup of liabilities and endowments, and construct a network of defaults. We then use Jiang-Lim-Yao-Ye to construct a global ranking from the defaults, which yields one way of quantifying {\textquoteleft}systemic importance{\textquoteright}.",
keywords = "Eisenberg-Noe, Finance, Hodge theory, Network clearing, Systemic risk",
author = "Schenck, {Henry Koewing} and Richard Sowers and Rui Song",
note = "Funding Information: 1 Department of Mathematics, Auburn University, Auburn, 36849, AL, United States of America 2 Department of Mathematics and Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, 61801, IL, United States of America 3 Department of Mathematics, University of Illinois, Urbana, 61801, IL, United States of America ∗ Schenck supported by NSF 1818646, Sowers supported by NSF 1727785. We thank Stevanovich Center for Financial Mathematics and the University of Chicago, where this work was presented in the conference {\textquoteleft}Geometry and Data Analysis{\textquoteright}. ∗∗ Author to whom should be corresponding address. Funding Information: Schenck supported by NSF 1 818 646, Sowers supported by NSF 1 727 785. We thank Stevanovich Center for Financial Mathematics and the University of Chicago, where this work was presented in the conference {\textquoteleft}Geometry and Data Analysis{\textquoteright}. Funding Information: Schenck supported by NSF 1818646, Sowers supported by NSF 1727785. We thank Stevanovich Center for Financial Mathematics and the University of Chicago, where this work was presented in the conference ?Geometry and Data Analysis?. Publisher Copyright: {\textcopyright} 2021 The Author(s). Published by IOP Publishing Ltd.",
year = "2021",
doi = "10.1088/2399-6528/abd1c2",
language = "English (US)",
volume = "5",
pages = "1--20",
journal = "Journal of Physics Communications",
issn = "2399-6528",
publisher = "Institute of Physics Publishing",
number = "1",
}