# The Leland-Toft optimal capital structure model under Poisson observations

## TL;DR

This paper extends the Leland-Toft optimal capital structure model by incorporating Poisson-based observation intervals, analyzing how delayed information impacts bankruptcy strategies, leverage, and credit spreads.

## Contribution

It introduces a novel model where asset information is observed at Poisson jump times, providing new insights into optimal bankruptcy timing under delayed information.

## Key findings

- Optimal bankruptcy strategy derived under Poisson observations
- Observation frequency significantly affects leverage and credit spreads
- Numerical analysis shows sensitivity of solutions to observation intervals

## Abstract

We revisit the optimal capital structure model with endogenous bankruptcy first studied by Leland \cite{Leland94} and Leland and Toft \cite{Leland96}. Differently from the standard case, where shareholders observe continuously the asset value and bankruptcy is executed instantaneously without delay, we assume that the information of the asset value is updated only at intervals, modeled by the jump times of an independent Poisson process. Under the spectrally negative L\'evy model, we obtain the optimal bankruptcy strategy and the corresponding capital structure. A series of numerical studies are given to analyze the sensitivity of observation frequency on the optimal solutions, the optimal leverage and the credit spreads.