Optimal dividends and capital injection: A general L\'evy model with extensions to regime-switching models

TL;DR

This paper analyzes optimal dividend and capital injection strategies within a general Le9vy process framework, extending results to regime-switching models and demonstrating the optimality of double barrier strategies in complex stochastic settings.

Contribution

It introduces a comprehensive analysis of optimal dividend strategies in a general Le9vy model, including regime-switching extensions, with proofs of strategy optimality under broad conditions.

Findings

Optimality of double barrier strategy in single-regime setting

Extension to Markov-modulated double barrier strategy in regime-switching models

Generalization to Le9vy processes with positive and negative jumps

Abstract

This paper studies a general L\'evy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in the single-regime setting with a concave terminal payoff function. This is then applied to show the optimality of a Markov-modulated double barrier strategy in the regime-switching model via contraction mapping arguments. We solve these for a general L\'evy model with both positive and negative jumps, greatly generalizing the existing results on spectrally one-sided models.