Hybrid fuzzy least-squares regression analysis in claims reserving with geometric separation method

Apaydin, Ayşen; Baser, Furkan

doi:10.1016/j.insmatheco.2010.07.001

Cited by 14 publications

(13 citation statements)

References 31 publications

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“…Option 3 Fuzzy Regression Methods (FRMs) have been applied in several actuarial issues to fit relevant variables [52] for a comprehensive description of application areas). In this way, [53] fits the term structure of interest rates, [54,55] predicts claim provisions, and [25,28] adjusts the Lee-Carter mortality law.…”

Section: Implementing a Markovian Fuzzy Bonus-malus System Governed Bmentioning

confidence: 99%

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

2021

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Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they are also used in many other fields ranging from economics, management, agricultural sciences, engineering or informatics to medicine. This paper focuses on the use of MCs for the design of non-life bonus-malus systems (BMSs). It proposes quantifying the uncertainty of transition probabilities in BMSs by using fuzzy numbers (FNs). To do so, Fuzzy MCs (FMCs) as defined by Buckley and Eslami in 2002 are used, thus giving rise to the concept of Fuzzy BMSs (FBMSs). More concretely, we describe in detail the common BMS where the number of claims follows a Poisson distribution under the hypothesis that its characteristic parameter is not a real but a triangular FN (TFN). Moreover, we reflect on how to fit that parameter by using several fuzzy data analysis tools and discuss the goodness of triangular approximates to fuzzy transition probabilities, the fuzzy stationary state, and the fuzzy mean asymptotic premium. The use of FMCs in a BMS allows obtaining not only point estimates of all these variables, but also a structured set of their possible values whose reliability is given by means of a possibility measure. Although our analysis is circumscribed to non-life insurance, all of its findings can easily be extended to any of the abovementioned fields with slight modifications.

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Section: Implementing a Markovian Fuzzy Bonus-malus System Governed Bmentioning

confidence: 99%

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

2021

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“…As shown in Table 1, among the most commonly used schemes for quantifying loss reserves, in addition to the CL method, we can highlight the geometric separation method [16] and methods that model incremental claims in a two-way manner, such as in [17]. The methodology for adjusting the parameters governing the evolution of claims over time can be performed heuristically [4,14,15,18] or with fuzzy regression methods that apply both the principle of minimum fuzziness [19,20] and the fuzzy least-squares approach [21,22]. Table 1.…”

Section: Introductionmentioning

confidence: 99%

Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method

Andrés-Sánchez

2024

Mathematics

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Estimating loss reserves is a crucial activity for non-life insurance companies. It involves adjusting the expected evolution of claims over different periods of active policies and their fluctuations. The chain-ladder (CL) technique is recognized as one of the most effective methods for calculating claim reserves in this context. It has become a benchmark within the insurance sector for predicting loss reserves and has been adapted to estimate variability margins. This variability has been addressed through both stochastic and possibilistic analyses. This study adopts the latter approach, proposing the use of the CL framework combined with intuitionistic fuzzy numbers (IFNs). While modeling with fuzzy numbers (FNs) introduces only epistemic uncertainty, employing IFNs allows for the representation of bipolar data regarding the feasible and infeasible values of loss reserves. In short, this paper presents an extension of the chain-ladder technique that estimates the parameters governing claim development through intuitionistic fuzzy regression, such as symmetric triangular IFNs. Additionally, it compares the results obtained with this method with those derived from the stochastic chain ladder by England and Verrall.

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“…But to integrate both fuzziness and randomness into a regression model, one should think about hybrid regression models. Apaydin and Baser (2010); Baser and Apaydin (2010) proposed a hybrid fuzzy least-squares regression (HFLSR) (Chang, 2001;Apaydin and Baser, 2010;Baser and Apaydin, 2010) analysis in claim reserving framework using a weighted function of fuzzy number (Yager and Filev, 1999).…”

Section: Introductionmentioning

confidence: 99%

“…However, the FRM developed in de Andrés Sánchez (2006); de Andrés-Sánchez (2007, 2012; de Andrés Sánchez (2014) and the HFLSR (Chang, 2001;Apaydin and Baser, 2010;Baser and Apaydin, 2010) as well don't select a proper value of h and is of the greatest importance. The criteria for selecting an h value are ad hoc (Moskowitz and Kim, 1993).…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Fuzzy Regression Model for Optimal Loss Reserving in Insurance

Apollinaire,

Doux,

Ronald

2018

Preprint

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In this article, a Hybrid Fuzzy Regression Model with Asymmetric Triangular Fuzzy Coefficients and optimized h−value in Generalized Linear Models (GLM) framework have been developed. The weighted functions of Fuzzy Numbers rather than the Expected value of Fuzzy Number is used as a defuzzification procedure. We perform the new model on a numerical data (Taylor and Ashe, 1983) to predict incremental payments in loss reserving. We prove that the new Hybrid Model with the optimized h−value produce better results than the classical GLM according to the Reserve Prediction Error and Reserve Standard Deviation.

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Hybrid fuzzy least-squares regression analysis in claims reserving with geometric separation method

Cited by 14 publications

References 31 publications

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method

A Hybrid Fuzzy Regression Model for Optimal Loss Reserving in Insurance

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