Optimal reinsurance under adjustment coefficient measure in a discrete risk model based on Poisson MA(1) process

Abstract

In this paper, we study the retention levels for combinations of quota-share and excess of loss reinsurance by maximizing the insurer's adjustment coefficient, which in turn minimizes the asymptotic result of ruin probability. Assuming that the premiums are determined by the expected value principle, we consider a discrete risk model, in which a dependence structure is introduced based on Poisson MA(1) process between the claim numbers for each period. The impact of dependence parameter on the adjustment coefficient is discussed and numerical examples are provided to illustrate the results obtained in this paper.

Ruin-based risk measures in discrete-time risk models

“…McKenzie (1988McKenzie ( , 2003 for other properties of the Poisson MA(1) discrete-time process. The risk model based on the Poisson MA(1) is examined in, e.g., Cossette et al ( 2010) and applied in the context of reinsurance by Zhang et al (2015). In the proof of the following proposition, we need the concordance order, also called correlation order by Denuit et al (2006).…”

Ruin Probability in a Correlated Aggregate Claims Model with Common Poisson Shocks: Application to Reinsurance

“…'s) with mean α ik which is dependent of N (k) (t). For other risk model linked with the thinning procedure, one can refer to Cossette et al (2010), Cossette et al (2011), Zhang et al (2013), and references therein. For i = 1, ..., n, it follows that N i (t) is a homogeneous Poisson process with rate λ i , where…”

Stochastic Models, Statistics and Their Applications

“…Recently, the INMA models based on the binomial thinning operation as defined in (1), have been extended to threshold INMA models, [31], INMA models with structural changes, [28] and Poisson combined INMA(q) models, [29]. Additionally, the INMA processes have been applied in the reinsurance context, namely on discrete risk models (see [5,6,10,17,30]).…”