A stochastic control problem with linearly bounded control rates in a Brownian model

TL;DR

This paper introduces a new class of optimal dividend strategies called delayed linear control strategies within a Brownian model, which are more realistic and include previously proposed strategies as special cases.

Contribution

It proves the optimality of delayed linear control strategies for a stochastic control problem with linearly bounded control rates, extending previous work with more practical dividend policies.

Findings

Optimality of delayed linear control strategies established

Includes previously proposed strategies as special cases

Provides a more realistic model for dividend payments

Abstract

Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a Brownian model, we prove the optimality of a member of a new family of control strategies called delayed linear control strategies, for which the controlled process is a refracted diffusion process. For some parameters specifications, we retrieve the strategy initially proposed by Avanzi & Wong (2012) to regularize dividend payments, which is more consistent with actual practice.