Modeling Financial System with Interbank Flows, Borrowing, and Investing

TL;DR

This paper develops a comprehensive stochastic control model of the financial system incorporating interbank flows, borrowing, and investing, with explicit solutions that can replicate phenomena like liquidity traps and default distributions.

Contribution

It introduces a generalized interbank flow model with explicit solutions for stochastic control problems, integrating central bank policies and risk management in a unified framework.

Findings

Explicit solutions for stochastic control problems in financial models.

Ability to replicate liquidity traps and analyze default distributions.

Insights into the impact of central bank policies on systemic stability.

Abstract

In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets. Each private actor aims to maximize its expected terminal logarithmic utility. The central bank, in turn, aims to control the overall economy by means of an exponential utility function. We solve all stochastic optimal control problems explicitly. We are able to recreate occasions such as liquidity trap. We study distribution of the number of defaults (net worth of a private actor going below a certain threshold).