# A lending scheme for a system of interconnected banks with probabilistic constraints of failure

## TL;DR

This paper develops a closed-form optimal control solution for interbank lending under probabilistic failure constraints, providing a method to assess systemic risk in interconnected banking networks.

## Contribution

It introduces a novel closed-form solution for optimal interbank lending with probabilistic failure constraints and a direct method to compute systemic relevance of banks.

## Key findings

- Closed-form solution for optimal control under failure probability constraints
- Method to compute systemic relevance parameters for banks
- Application to real banking networks

## Abstract

We derive a closed form solution for an optimal control problem related to an interbank lending schemes subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived solution applies to a real banks network by obtaining a general solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network.