Paper: arXiv 2507.16494

Authors: Deb Narayan Barik, Siddhartha P. Chakrabarty

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 $DistancetoDefault$, 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.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a solid theoretical dynamic portfolio optimization framework using Hamilton-Jacobi-Bellman (HJB) equations and Vasicek interest rate dynamics to evaluate limited liability. However, it lacks empirical backtesting or real-world financial data, relying purely on theoretical proofs and stylistic numerical illustrations.

Research Flowchart

  flowchart TD
    A["Goal: Analyze Impact of Limited Liability (LL) on Bank Stability"] --> B["Build Continuous-Time Portfolio Models (With vs. Without LL)"]
    B --> C["Method: Approximate LL Payoff Function to Obtain Closed-Form Solutions"]
    D["Inputs: Vasicek Interest Rate Model & KMV Distance to Default Metric"] --> E["Compute Bank Resiliency & Asset Risk Profiles"]
    C --> E
    E --> F["Numerical Example & Simulation"]
    F --> G["Findings: LL Reduces Risky Asset Holdings & Increases Bank Stability"]

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0 of 46 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.