Risk models based on time series for count random variables

Cossette, Hélène; Marceau, Étienne; Toureille, Florent

doi:10.1016/j.insmatheco.2010.08.007

Cited by 20 publications

(10 citation statements)

References 11 publications

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“…'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…”

Section: The Risk Modelmentioning

confidence: 99%

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

Zhang

2015

Methodol Comput Appl Probab

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This paper considers a correlated aggregate claims model with common Poisson shocks, which allows for dependence in n (n ≥ 2) classes of business across m (m ≥ 1) different types of stochastic events. The dependence structure between different claim numbers is connected with the thinning procedure. Under combination of quota-share and excess of loss reinsurance arrangements, we examine the properties of the proposed risk model. An upper bound for the ruin probability determined by the adjustment coefficient is established through martingale approach. We reduce the problem of optimal reinsurance strategy for maximizing the insurer's adjustment coefficient and illustrate the results by numerical examples.

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Section: The Risk Modelmentioning

confidence: 99%

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

Zhang

2015

Methodol Comput Appl Probab

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“…They introduce the integer-valued autoregressive process with unobserved heterogeneity to explain the effects of the claim histories on the predictive premium. Cossette et al (2010Cossette et al ( , 2011 further develop the application of the integer-valued time series in discrete-time risk models. They extend the classical risk model for capturing serial dependence structures and calculate various quantities that are often concerned in risk theory to assess the riskiness of an insurance portfolio.…”

Section: Introductionmentioning

confidence: 99%

A combined integer-valued autoregressive process with actuarial applications

Yao

2023

Preprint

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This paper proposes a modification of a combined integer-valued autoregressive (CINAR) process based on binomial thinning, which is instrumental in modelling higher-order dependence between the number of claims in an insurance portfolio. The modified CINAR process is more general and enjoys stationarity and flexibility in higher-order serial dependence modelling. Two actuarial applications of the proposed process in risk theory and credibility model are explored. As an application to risk theory, we derive the distribution of aggregate claims under a discrete-time collective risk model and examine the effect of high-order dependence on the tail-related risk measures of the aggregate claims. Next, we apply the modified CINAR process to account for the unobserved gamma heterogeneity in determining the dynamics of the predictive credibility premium. A real data analysis shows that our approach provides a superior pattern to the predictive premium calculation when compared to the outcomes of several alternative models.

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“…Among them, Gourieroux and Jasiak (2004) reveal that the integer-valued autoregressive process of order 1 (INAR(1)) can be an acceptable alternative for modeling time dependence between the number of claims. Cossette et al (2010Cossette et al ( , 2011 extend the classical discrete-time risk model by introducing a dependence relationship in time between the number of claims. They use the Poisson INAR(1) process and the Poisson integer-valued moving average (INMA) process.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Distributions With Time and Cross-Dependence: Aggregation and Capital Allocation

Zhang²

2022

ASTIN Bull.

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This paper investigates risk aggregation and capital allocation problems for an insurance portfolio consisting of several lines of business. The class of multivariate INAR(1) processes is proposed to model different sources of dependence between the number of claims of the portfolio. The total capital required for the whole portfolio is evaluated under the TVaR risk measure, and the contribution of each line of business is derived under the TVaR-based allocation rule. We provide the risk aggregation and capital allocation formulas in the general case of continuous and strictly positive claim sizes and then in the case of mixed Erlang claim sizes. The impact of both time dependence and cross-dependence on the behavior of risk aggregation and capital allocation is numerically illustrated.

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Risk models based on time series for count random variables

Cited by 20 publications

References 11 publications

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

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

A combined integer-valued autoregressive process with actuarial applications

Multivariate Distributions With Time and Cross-Dependence: Aggregation and Capital Allocation

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