Loading...

Ratio-balanced maximum flows

Akrami, H ; Sharif University of Technology | 2019

385 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.ipl.2019.06.003
  3. Publisher: Elsevier B.V , 2019
  4. Abstract:
  5. When a loan is approved for a person or company, the bank is subject to credit risk; the risk that the lender defaults. To mitigate this risk, a bank will require some form of security, which will be collected if the lender defaults. Accounts can be secured by several securities and a security can be used for several accounts. The goal is to fractionally assign the securities to the accounts so as to balance the risk. This situation can be modeled by a bipartite graph. We have a set S of securities and a set A of accounts. Each security has a value vi and each account has an exposure ej. If a security i can be used to secure an account j, we have an edge from i to j. Let fij be the part of security i's value used to secure account j. We are searching for a maximum flow that sends at most vi units out of node i∈S and at most ej units into node j∈A. Then sj=ej−∑ifij is the unsecured part of account j and rj=sj/ej is the risk ratio of account j. Balancing the risk means to determine a maximum flow with the following property: if fij>0 and there is an edge from i to ℓ then rj≥rℓ. In particular, if fij>0 and fiℓ>0 then rj=rℓ. We give a polynomial time algorithm for finding such a maximum flow and also give an alternative characterization of the risk balancing maximum flow. It is the maximum flow minimizing ∑jrj 2ej. © 2019 Elsevier B.V
  6. Keywords:
  7. Graph algorithms ; Maximum flows ; Polynomial time ; Ratio-balanced ; Finance ; Polynomial approximation ; Risk assessment ; Bipartite graphs ; Credit risks ; Polynomial-time algorithms ; Flow graphs
  8. Source: Information Processing Letters ; Volume 150 , 2019 , Pages 13-17 ; 00200190 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0020019019301024