The Absolute Ruin Insurance Risk Model with a Threshold Dividend Strategy

Wenguang Yu,Yujuan Huang,Chaoran Cui

doi:10.3390/sym10090377

Abstract

The absolute ruin insurance risk model is modified by including some valuable market economic information factors, such as credit interest, debit interest and dividend payments. Such information is especially important for insurance companies to control risks. We further assume that the insurance company is able to finance and continue to operate when its reserve is negative. We investigate the integro-differential equations for some interest actuarial diagnostics. We also provide numerical examples to explain the effects of relevant parameters on actuarial diagnostics.

Highlights

Consider the classical insurance risk model, the cash flow of company is modeled by the risk reserve process { Rut ; t ≥ 0}, with
In order to make the risk model closer to the actual operating situation, we added three other properties related to the risk reserve process (1), namely, debit interest, credit interest and dividend payments
The results can be compared to the results of Peng et al [5] who considered a compound Poisson risk model with a constant dividend barrier and liquid reserves in the case of absolute ruin

Summary

Introduction

Consider the classical insurance risk model, the cash flow of company is modeled by the risk reserve process { Rut ; t ≥ 0}, with. Wang et al [6] further considered a threshold dividend barrier under the absolute ruin risk model. Li and Lu [7] further explored the case of the Markov-dependent risk model under absolute ruin. The present value of all dividends until absolute ruin time is given by. The results can be compared to the results of Peng et al [5] who considered a compound Poisson risk model with a constant dividend barrier and liquid reserves in the case of absolute ruin. We obtained the conclusion that the influence of parameter b on the moment of the present value of all dividends until absolute ruin is the same, regardless of whether a constant dividend barrier or the threshold dividend strategy is used. The results show that W13 (u, b) decreases as b, α, and β increase but increases as u increases

The Gerber-Shiu Expected Discounted Penalty Function

The Laplace Transform of Absolute Ruin Time

The Time to Reach the Dividend Barrier