Optimal bail-out dividends problem with transaction cost and capital injection constraint

TL;DR

This paper analyzes the optimal bail-out dividend problem with transaction costs and capital injection constraints in a Lévy risk model, providing explicit policy characterizations and numerical illustrations.

Contribution

It introduces a comprehensive solution framework for the bail-out dividend problem with transaction costs and capital constraints, including the optimality of reflected (c1; c2)-policies and dual problem analysis.

Findings

Optimality of reflected (c1; c2)-policies established

Dual Lagrangian problem characterized with slackness conditions

Numerical examples illustrate the theoretical results

Abstract

We consider the bail-out optimal dividend problem under fixed transaction costs for a L\'evy risk model. Furthermore, we consider the version with a constraint expected net present value of injected capital. To characterize the solution to the aforementioned models, we first solve the bail-out optimal dividend problem under transaction costs and capital injection and show the optimality of reflected (c1; c2)- policies. Next, we introduce the dual Lagrangian problem and show that the complementary slackness conditions are satisfied, characterizing the optimal Lagrange multiplier. Finally, we illustrate our findings with a series of numerical examples.