Equilibrium Defaultable Corporate Debt and Investment
Abstract
In dynamic capital structure models with an investor break-even condition, the firm's Bellman equation may not generate a contraction mapping, so the standard existence and uniqueness conditions do not apply. First, we provide an example showing the problem in a classical trade-off model. The firm can issue one-period defaultable debt, invest in capital and pay a dividend. If the firm cannot meet the required debt payment, it is liquidated. Second, we show how to use a dual to the original problem and a change of measure, such that existence and uniqueness can be proved. In the unique Markov-perfect equilibrium, firm decisions reflect state-dependent capital and debt targets. Our approach may be useful for other dynamic firm models that have an investor break-even condition.
Keywords
Cite
@article{arxiv.2202.05885,
title = {Equilibrium Defaultable Corporate Debt and Investment},
author = {Hong Chen and Murray Zed Frank},
journal= {arXiv preprint arXiv:2202.05885},
year = {2022}
}