Can Limited Liability Increase Stability for Banks: A Dynamic Portfolio Approach

TL;DR

This paper introduces a dynamic portfolio model for banks that incorporates limited liability, demonstrating that it leads to less risky asset choices and enhances bank resilience, supported by analytical and numerical analysis.

Contribution

It develops a novel continuous-time model including limited liability in the bank's decision-making process, showing its impact on risk and resilience.

Findings

Limited liability results in less risky asset portfolios.

Inclusion of limited liability increases bank resilience.

Numerical examples confirm theoretical predictions.

Abstract

We present a novel approach for the bank's decision problem, incorporating Limited Liability in the objective function. Accordingly, we consider continuous time models, with and without Limited Liability. We compare the solutions of these two models to demonstrate the effect of inclusion of Limited Liability. To solve the problem with the objective function incorporating Limited Liability, we approximate the payoff function to another set of functions for which we have closed-form solutions. Then, we show that the solution with Limited Liability incorporates less risky assets, while simultaneously increasing the resilience of the bank. After that, we use the metric of $Distance~to~Default$, from the KMV Model, to analyze the bank's resiliency, by considering that the interest rate follows the Vasicek model. Finally, we illustrate the results obtained with a numerical example.