On the Dividend Strategies with Non-Exponential Discounting

TL;DR

This paper investigates optimal dividend strategies under non-constant discount rates in a diffusion risk model, addressing time inconsistency and deriving equilibrium strategies using extended HJB equations.

Contribution

It introduces a framework for analyzing dividend strategies with non-exponential discounting and provides explicit solutions for pseudo-exponential discount functions.

Findings

Derived equilibrium dividend strategies for pseudo-exponential discount functions

Established verification theorem for general discount functions

Extended HJB equations characterize time-inconsistent control problems

Abstract

In this paper, we study the dividend strategies for a shareholder with non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to the Markov strategies. This is a time inconsistent control problem. The extended HJB equation is given and the verification theorem is proved for a general discount function. Considering the pseudo-exponential discount functions (Type I and Type II), we get the equilibrium dividend strategies and the equilibrium value functions by solving the extended HJB equations.