Time-inconsistent view on a dividend problem with penalty

TL;DR

This paper studies a time-inconsistent dividend maximization problem with a penalty term, deriving explicit equilibrium strategies in a diffusion model and illustrating the results with a numerical example.

Contribution

It introduces a novel approach to handling time-inconsistency in dividend problems by using different discount rates and derives explicit equilibrium strategies.

Findings

Explicit equilibrium dividend strategy derived

The value function associated with the strategy is characterized

Numerical example illustrates the theoretical results

Abstract

We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the dividends and the penalty, which causes time-inconsistency. This allows to study different types of constraints. For the diffusion approximation of the classical surplus process we derive an explicit equilibrium dividend strategy and the associated value function. Inspired by duality arguments, we can identify a particular equilibrium strategy such that for a given initial surplus the imposed constraint is fulfilled. Furthermore, we illustrate our findings with a numerical example.