Linear Models (Loss Reserving)

Schmidt, Klaus D.

doi:10.1007/978-3-319-30056-6_18

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…The historical data illustrating the evolution of claims are typically presented in a run-off triangle format similar to that shown in Table 2 [61]. In this table, Z i,j represents the accumulated claim cost of insurance contracts originating in the ith development period (i = 0, 1. .…”

Section: Intuitionistic Linear Regression With the Minimum Fuzziness ...mentioning

confidence: 99%

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Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

De Andrés-Sánchez

2024

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A highly relevant topic in the actuarial literature is so-called “claim reserving” or “loss reserving”, which involves estimating reserves to be provisioned for pending claims, as they can be deferred over various periods. This explains the proliferation of methods that aim to estimate these reserves and their variability. Regression methods are widely used in this setting. If we model error terms as random variables, the variability of provisions can consequently be modelled stochastically. The use of fuzzy regression methods also allows modelling uncertainty for reserve values using tools from the theory of fuzzy subsets. This study follows this second approach and proposes projecting claim reserves using a generalization of fuzzy numbers (FNs), so-called intuitionistic fuzzy numbers (IFNs), through the use of intuitionistic fuzzy regression. While FNs allow epistemic uncertainty to be considered in variable estimation, IFNs add bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis is grounded in the ANOVA two-way framework, which is adapted to the use of intuitionistic regression. Similarly, we compare our results with those obtained using deterministic and stochastic chain-ladder methods and those obtained using two-way statistical ANOVA.

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Section: Intuitionistic Linear Regression With the Minimum Fuzziness ...mentioning

confidence: 99%

“…., n are unknown and must be fitted. The run-off triangle of accumulated claims (Table 2) shows the input of several classical methods to fit claim reserves, such as a chain ladder [61]. The key concept of the chain ladder is the so-called link ratio or development ratio between the payment periods j and j + 1 ( f j ):…”

Section: Development/payment Periodmentioning

confidence: 99%

Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

De Andrés-Sánchez

2024

Axioms

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“…Reserving for claims that have been incurred but not reported is a fundamental task of actuaries within non-life insurance companies, primarily to ensure the company’s current and future ability to meet policy holder claims, but also to allow for the up to date tracking of loss ratios on an accident and underwriting year basis, which is essential for the provision of accurate management information. Since Bornhuetter and Ferguson (1972) encouraged actuaries to pay attention to the topic of IBNR reserves, a vast literature on loss reserving techniques has emerged; see, for example, Schmidt (2017) and Wüthrich and Merz (2008). Nonetheless, the relatively more simple chain-ladder method remains the most popular choice of method for actuaries reserving for short-term insurance liabilities, globally and in South Africa (Dal Moro et al , 2016).…”

Section: Survey Of Deep Learning In Actuarial Sciencementioning

confidence: 99%

AI in actuarial science – a review of recent advances – part 2

Richman

2020

Ann. actuar. sci.

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Rapid advances in artificial intelligence (AI) and machine learning are creating products and services with the potential not only to change the environment in which actuaries operate, but also to provide new opportunities within actuarial science. These advances are based on a modern approach to designing, fitting and applying neural networks, generally referred to as “Deep Learning”. This paper investigates how actuarial science may adapt and evolve in the coming years to incorporate these new techniques and methodologies. Part 1 of this paper provides background on machine learning and deep learning, as well as an heuristic for where actuaries might benefit from applying these techniques. Part 2 of the paper then surveys emerging applications of AI in actuarial science, with examples from mortality modelling, claims reserving, non-life pricing and telematics. For some of the examples, code has been provided on GitHub so that the interested reader can experiment with these techniques for themselves. Part 2 concludes with an outlook on the potential for actuaries to integrate deep learning into their activities. Finally, a supplementary appendix discusses further resources providing more in-depth background on machine learning and deep learning.

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“…For example, Braun (2004) showed the effectiveness of the multivariate chain-ladder method using simulated data, demonstrating an increased estimation accuracy of the prediction error when accounting for the correlation between loss triangles. Merz and Wüthrich (2008) also studied the prediction error of a modified multivariate chain-ladder model proposed by Schmidt (2006) and incorporated a dependence structure into their model.…”

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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Linear Models (Loss Reserving)

Cited by 4 publications

References 20 publications

Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

AI in actuarial science – a review of recent advances – part 2

Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves

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