Tweedie double GLM loss triangles with dependence within and across business lines

Iturria, Carlos Andrés Araiza; Godin, Frédéric; Mailhot, Mélina

doi:10.1007/s13385-021-00267-0

Cited by 5 publications

(1 citation statement)

References 19 publications

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“…More recently, Shi (2017) conducted an analysis of multiple inter-company loss triangles using the Bayesian hierarchical model. Avanzi et al (2016) introduced a multivariate Tweedie approach to capture cell-wise dependence in loss reserving, while Araiza Iturria et al (2021) presented a stochastic model aimed at capturing dependencies between loss triangles. In their work, they opted for a Tweedie-distributed double-generalized linear model to represent the marginal distribution.…”

Section: Introductionmentioning

confidence: 99%

Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves

Abdallah,

Wang

2023

Risks

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The interdependence between multiple lines of business has an important impact on determining loss reserves and risk capital, which are crucial for the solvency of a property and casualty (P&C) insurance company. In this work, we introduce the two-stage inference method using the Sarmanov family of multivariate distributions to the actuarial literature. In fact, we study rank-based methods using the Sarmanov distribution to adequately estimate the loss reserves and properly capture the dependence between lines of business. An inadequate choice of the dependence structure may negatively impact the estimation of the marginals and, hence, the reserve. Thus, we propose a two-stage inference strategy in this research to address this, while taking advantage of the flexibility of the Sarmanov distribution. We show that this strategy leads to a more robust estimation, and better captures the dependence between the risks. We also show that it generates smaller risk capital and a better diversification benefit. We extend the model to the multivariate case with more than two lines of business. To illustrate and validate our methods, we use three different sets of real data from both a major US property–casualty insurer and a large Canadian insurance company.

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Section: Introductionmentioning

confidence: 99%

Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves

Abdallah,

Wang

2023

Risks

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One-year and ultimate correlations in dependent claims run-off triangles

Delong,

Szatkowski

2024

Ann. actuar. sci.

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We investigate bottom-up risk aggregation applied by insurance companies facing reserve risk from multiple lines of business. Since risk capitals should be calculated in different time horizons and calendar years, depending on the regulatory or reporting regime (Solvency II vs IFRS 17), we study correlations of ultimate losses and correlations of one-year losses in future calendar years in lines of business. We consider a multivariate version of a Hertig’s lognormal model and we derive analytical formulas for the ultimate correlation and the one-year correlations in future calendar years. Our main conclusion is that the correlation coefficients that should be used in a bottom-up aggregation formula depend on the time horizon and the future calendar year where the risk emerges. We investigate analytically and numerically properties of the ultimate and the one-year correlations, their possible values observed in practice, and the impact of misspecified correlations on the diversified risk capital.

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Estimating Risk Relativity of Driving Records using Generalized Additive Models: A Statistical Approach for Auto Insurance Rate Regulation

Xie

2023

Asia-Pacific Journal of Risk and Insurance

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Studying driving records (DR) and assessing their risk relativity is crucial for auto insurance rate regulation. Typically, the evaluation of DR involves estimating risk using empirical loss cost or modeling approaches such as Generalized Linear Models (GLM). This article presents a novel methodology employing Generalized Additive Models (GAM) to estimate the risk relativity of DR. By treating the integer level of DR as a continuous variable, the proposed method offers enhanced flexibility and practicality in evaluating the associated risk. Extending the linear model to GAM is a critical advancement that harnesses advanced statistical methods in actuarial practice, providing a more statistically robust application of the proposed approach. Moreover, the integration of functional patterns with Class or Territory enables the investigation of statistical evidence supporting the existence of associations between risk factors. This approach helps address the issue of potential double penalties in insurance pricing and calls for a statistical solution to overcome this challenge. Our study demonstrates that utilizing the GAM approach yields a more balanced estimation of DR relativity, thereby reducing discrimination among different DR levels. This finding highlights the potential of this statistical method to improve fairness and accuracy in auto insurance rate making and regulation.

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Tweedie double GLM loss triangles with dependence within and across business lines

Cited by 5 publications

References 19 publications

Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves

Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves

One-year and ultimate correlations in dependent claims run-off triangles

Estimating Risk Relativity of Driving Records using Generalized Additive Models: A Statistical Approach for Auto Insurance Rate Regulation

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