Optimal dividends in a discrete-time dual risk model with stochastic expenses

Li Deng; Zhichao Chen; Li Deng; Zhichao Chen

doi:10.3934/math.20241524

AIMS Mathematics

2024, Volume 9, Issue 11: 31696-31720. doi: 10.3934/math.20241524

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Research article

Optimal dividends in a discrete-time dual risk model with stochastic expenses

Li Deng ^1,3,
Zhichao Chen ^{2
,
,}

1.
School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
2.
School of Intelligent Engineering, Shaoguan University, Shaoguan 512005, China
3.
School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China

Received: 02 September 2024 Revised: 21 October 2024 Accepted: 30 October 2024 Published: 07 November 2024
MSC : 49M25, 60G51, 93E20

Dividend policies play a pivotal role in financial management by aiming to maximize shareholders' interest and effectively managing risk. In this paper, we explore the optimal dividend strategy in a discrete-time compound binomial dual risk framework. This model is suitable for a company whose income comes from occasional operating expenses and settlements only once per unit of time. We assume that expenses are subject to dynamic changes influenced by economic factors, following a Markov chain. With or without a ceiling constraint on dividend payments, we prove that the optimal value function serves as the exclusive solution to a discrete Hamilton-Jacobi-Bellman (HJB) equation through the utilization of the fixed-point theorem. Furthermore, we derive a straightforward computational approach for determining the optimal strategy. Finally, we provide numerical examples to illustrate the theoretical findings and calculation methods.
- optimal dividend strategy,
- dual risk model,
- stochastic expenses,
- HJB equation,
- fixed-point theorem
Citation: Li Deng, Zhichao Chen. Optimal dividends in a discrete-time dual risk model with stochastic expenses[J]. AIMS Mathematics, 2024, 9(11): 31696-31720. doi: 10.3934/math.20241524

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Abstract

Dividend policies play a pivotal role in financial management by aiming to maximize shareholders' interest and effectively managing risk. In this paper, we explore the optimal dividend strategy in a discrete-time compound binomial dual risk framework. This model is suitable for a company whose income comes from occasional operating expenses and settlements only once per unit of time. We assume that expenses are subject to dynamic changes influenced by economic factors, following a Markov chain. With or without a ceiling constraint on dividend payments, we prove that the optimal value function serves as the exclusive solution to a discrete Hamilton-Jacobi-Bellman (HJB) equation through the utilization of the fixed-point theorem. Furthermore, we derive a straightforward computational approach for determining the optimal strategy. Finally, we provide numerical examples to illustrate the theoretical findings and calculation methods.

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