On a Discrete-Time Risk Model with Random Income and a Constant Dividend Barrier

Zhenhua Bao,Jing Wang,Junqing Huang,Xuewen Lu

doi:10.1155/2021/5575187

Abstract

In this paper, a discrete-time risk model with random income and a constant dividend barrier is considered. Under such a dividend policy, once the insurer’s reserve hits the level b b > 0 , the excess of the reserve over b is paid off as dividends. We derive a homogeneous difference equation for the expected present value of dividend payments. Corresponding solution procedures for the difference equation are invested. Finally, we give a numerical example to illustrate the applicability of the results obtained.

Highlights

Many authors focus their research interests on discrete-time risk models, which can be used as an approximation to continuous time models
Discrete-time risk models with dependent structure have received increasing attention, and the readers are referred to Liu and Bao [2] for the related studies on different kinds of dependent models
We introduce a dividend policy to the company that a certain amount of dividends will be paid to the policyholder instantly, as long as the surplus of the company at time k is higher than a constant dividend barrier b(b > 0)

Summary

Introduction

Many authors focus their research interests on discrete-time risk models, which can be used as an approximation to continuous time models. For the compound binomial risk model with possible delay of claims, Xie and Zou [5] investigate the expected present value of total dividends under stochastic interest rates. We propose a discrete-time risk model with random income and a constant dividend barrier. We introduce a dividend policy to the company that a certain amount of dividends will be paid to the policyholder instantly, as long as the surplus of the company at time k is higher than a constant dividend barrier b(b > 0) It implies that the dividend payments will only possibly occur at the beginning of each period, right after receiving the premium payment.

Expected Present Value of Dividend Payments

Numerical Example

Concluding Remarks