hu / en

Uniqueness of Clearing Payment Matrices in Financial Networks – by Péter Csóka – P. Jean-Jacques Herings

 

Uniqueness of Clearing Payment Matrices in Financial Networks

 
Mathematics of Operations Research – Published Online:

Abstract

We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest clearing payment and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present a new condition for uniqueness that generalizes all the existing conditions proposed in the literature. Our condition depends on the decomposition of the financial network into strongly connected components. A strongly connected component that contains more than one agent is called a cycle, and the involved agents are called cyclical agents. If there is a cycle without successors, then one of the agents in such a cycle should have a strictly positive endowment. The division rule used by a cyclical agent with a strictly positive endowment should be positive monotonic, and the rule used by a cyclical agent with a zero endowment should be strictly monotonic. Because division rules involving priorities are not positive monotonic, uniqueness of the clearing payment matrix is a much bigger concern for such division rules than for proportional ones. As a final contribution of the paper, we exhibit the relationship between the uniqueness of clearing payment matrices and the continuity of bankruptcy rules, a property that is very much desired for stability of financial systems.

Funding: This research was supported by the Higher Education Institutional Excellence Program 2020 of the Ministry of Innovation and Technology in the framework of the “Financial and Public Services” research project [Grant TKP2020-IKA-02] at Corvinus University of Budapest. P. Csóka received funding from the National Research, Development and Innovation Office [Grants K-120035 and K-138826].

2024

Jun

13

M

T

W

T

F

S

S

27

28

29

30

31

1

2

3

4

5

7

8

9

10

11

12

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

1

2

3

4

5

6

7

Next month >