Ruin-based risk measures in discrete-time risk models

Cossette, Hélène; Marceau, Étienne; Trufin, Julien; Zuyderhoff, Pierre

doi:10.1016/j.insmatheco.2020.05.003

Cited by 7 publications

(2 citation statements)

References 58 publications

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“…Considering that an insurance portfolio may contain several lines of business, Bermúdez et al (2018) adopt bivariate integer-valued time series to price an automobile insurance contract with two types of coverage, taking into account the dependence structures arising from different sources of the number of claims. For more details on the integer-valued time series and applications in actuarial science, we refer to Zhang et al (2015), Hu et al (2018), Cossette et al (2020), Guan and Hu (2022) and Hu and Zhang (2022) and the references therein.…”

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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Section: Introductionmentioning

confidence: 99%

A combined integer-valued autoregressive process with actuarial applications

Yao

2023

Preprint

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“…They use the Poisson INAR(1) process and the Poisson integer-valued moving average (INMA) process. See, also, Zhang et al (2015) and Cossette et al (2020) for further details on univariate integer-valued time series with applications in actuarial science. At the same time, an insurance portfolio may contain several lines of business.…”

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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On the evaluation of risk models with bivariate integer-valued time series

Chen

2021

Lith Math J

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Ruin-based risk measures in discrete-time risk models

Cited by 7 publications

References 58 publications

A combined integer-valued autoregressive process with actuarial applications

A combined integer-valued autoregressive process with actuarial applications

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

On the evaluation of risk models with bivariate integer-valued time series

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