# Impulse control in a spectrally negative L\'evy model with a level-dependent intensity of bankruptcy

## TL;DR

This paper studies an optimal dividend strategy in a spectrally negative Lévy process with bankruptcy penalties, identifying optimal thresholds and providing a numerical method for their computation.

## Contribution

It introduces a novel model incorporating state-dependent bankruptcy penalties and characterizes the optimal dividend strategy with unique thresholds.

## Key findings

- Optimal thresholds for dividend payments are identified.
- The model accounts for bankruptcy penalties based on surplus levels.
- A numerical method for computing optimal thresholds is developed.

## Abstract

We consider an optimal dividend problem with transaction costs where the surplus is modelled by a spectrally negative L\'evy process in an Omega model. n this model, the surplus is allowed to spend time below the critical ruin level, but is penalised by a state-dependent intensity of bankruptcy. We show that under the spectrally negative model an optimal strategy is such that the surplus is reduced to a level $c_1$ whenever they are above another level $c_2$, and that such levels are unique under the additional assumption that the L\'evy measure has a log-convex tail. We describe a numerical method to compute the optimal values $c_1$ and $c_2$.