On Periodic Dividends for the Classical Risk Model with Debit Interest

Hua Dong,Xianghua Zhao

doi:10.1155/2020/6395717

Abstract

A periodic dividend problem is studied in this paper. We assume that dividend payments are made at a sequence of Poisson arrival times, and ruin is continuously monitored. First of all, three integro-differential equations for the expected discounted dividends are obtained. Then, we investigate the explicit expressions for the expected discounted dividends, and the optimal dividend barrier is given for exponential claims. A similar study on a generalized Gerber–Shiu function involving the absolute time is also performed. To demonstrate the existing results, we give some numerical examples.

Highlights

Suppose the dynamics of the surplus process of an insurance company at time t is defined as the solution to
Where c > 0 is the premium charged in the unit time and α > 0 is the debit interest
St 􏽐Ni (1t) Xi is a compound Poisson process with intensity c > 0 representing the total claim amounts until time t, and Xi is the i − th claim size

Summary

Introduction

Suppose the dynamics of the surplus process of an insurance company at time t is defined as the solution to⎧⎪⎪⎪⎨ cdt − dSt, Rt ≥ 0, dRt ⎪⎪⎪⎩ c + αRt􏼁dt − dSt, c − α ≤ Rt < 0, (1)where c > 0 is the premium charged in the unit time and α > 0 is the debit interest. Considering dividends can only be made at some discrete times in practice, Albrecher et al [6] put forward the periodic barrier dividends in this type of risk model. Ey assumed that both barrier dividends and ruin can only be observed at some randomized times.

Results

Conclusion