Title: How many banks do you need to multiply two numbers?
We consider the problem of clearing a system of interconnected financial
institutions that have been exposed to a shock on their assets. In prior
work we have shown that if banks can enter into both debt contracts and
credit default swaps (CDSs) and banks incur a cost upon
default, then a solution to the clearing problem may not exist and it is
NP-hard to decide if it does.
In our current work, we complement these results by showing that without
default costs, a solution always exists, but actually computing an
(approximate) solution is PPAD-hard.
To show this, we demonstrate how financial networks with CDSs can express
arithmetic operations such as addition and multiplication.
Our result contrasts with previous work on debt-only financial networks,
in which a solution can always be found in polynomial time.
In this talk, I would like to discuss with you the assumptions and
economic implications of my theorem as well as potential extensions.
I will also provide an introduction to the PPAD complexity class.