Ruin Analysis on a New Risk Model with Stochastic Premiums and Dependence Based on Time Series for Count Random Variables

Abstract

In this paper, we propose a new discrete-time risk model of an insurance portfolio with stochastic premiums, in which the temporal dependence among the premium numbers of consecutive periods is fitted by the first-order integer-valued autoregressive (INAR(1)) process and the temporal dependence among the claim numbers of consecutive periods is described by the integer-valued moving average (INMA(1)) process. To measure the risk of the model quantitatively, we study the explicit expression for a function whose solution is defined as the Lundberg adjustment coefficient and give the Lundberg approximation formula for the infinite-time ruin probability. In the case of heavy-tailed claim sizes, we establish the asymptotic formula for the finite-time ruin probability via the large deviations of the aggregate claims. Two numerical examples are provided in order to illustrate our theoretical findings.

Determining Safe Withdrawal Rates for Post-Retirement via a Ruin-Theory Approach

“…Also, general references on copulas are Joe (1997) and Nelsen (2007) among others. On the other hand, in Zhang and Yang (2010), Xie and Zou (2013), Vidmar (2018), and Guan and Wang (2023), some dependency structures and different approaches to consider them are investigated.…”

“…Also, the study yields a clear expression for the ruin probability when both claim and premium sizes follow exponential distributions. Guan and Wang (2023) examine the dependence between premium numbers in consecutive periods and claim numbers in consecutive periods using integer-valued auto-regressive (IVAR(1)) and integer-valued moving average (INMA(1)) processes. Additionally, the authors establish an asymptotic formula for the finite-time ruin probability by studying the large deviations of the aggregate claims.…”