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Journal articles on the topic 'Run-off triangle'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 January 2023

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1

Barlak, Jan, Matus Bakon, Martin Rovnak, and Martina Mokrisova. "Heat Equation as a Tool for Outliers Mitigation in Run-Off Triangles for Valuing the Technical Provisions in Non-Life Insurance Business." Risks 10, no. 9 (August 28, 2022): 171. http://dx.doi.org/10.3390/risks10090171.

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Estimating outstanding claims reserves in the non-life insurance business is often impaired by outlier-contaminated datasets. Widely used methods to eliminate outliers in non-life development triangles are either limiting the number of outliers by robust statistical methods or by change of development factors. However, the whole estimation process is likewise adversely affected so that: (i) the total sum of all triangle payments is not correct or (ii) the difference between the original triangle and its backward estimation via the bootstrap method is ineligible. In this paper, the properties of the heat equation are examined to obtain an outlier smoothing technique for development triangles. The heat equation in two dimensions is being applied on an outlier contaminated dataset where no individual data are available. As a result, we introduce a new methodology to (i) treat outliers in non-life development triangles, (ii) keep the total sum of all triangle payments, and (iii) provide acceptable differences between the original and the backward estimated triangle. Consequently, the outlying values are eliminated and the resulting development triangle could be used as an input for any claims reserving method without a need for further robustification or change of development factors. Additionally, the research on the application of heat equation in one dimension presented in this paper enables one to employ the bootstrap method using Pearson’s residuals in cases where the method was originally inapplicable due to development factors being lower than one.

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2

Pater, Roelf. "The run-off-triangle: Least squares — against chainladder estimations." Blätter der DGVFM 19, no. 1 (April 1989): 11–17. http://dx.doi.org/10.1007/bf02809466.

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3

IDO, Shunsuke, Masanori MICHIUE, Kuniaki MIYAMOTO, and Osamu HINOKIDANI. "RUN-OFF ANALYSIS METHOD OF SURFACE-SUBSURFACE WATER FLOW USING TRIANGLE SCHEME." PROCEEDINGS OF HYDRAULIC ENGINEERING 46 (2002): 157–62. http://dx.doi.org/10.2208/prohe.46.157.

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4

Amini, Raisha, and Yulial Hikmah. "ESTIMASI CADANGAN KLAIM IBNR MENGGUNAKAN METODE CHAIN-LADDER DAN BORNHUETTER-FERGUSON PADA PRODUK INDEMNITY DI PT. XYZ." MAp (Mathematics and Applications) Journal 4, no. 1 (June 30, 2022): 50–59. http://dx.doi.org/10.15548/map.v4i1.4203.

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Klaim IBNR (Incurred But Not Reported) adalah klaim yang sudah terjadi namun belum dilaporkan. Karena belum dilaporkan, maka totalnya diakumulasikan dalam bentuk cadangan dan dianggap sebagai kewajiban bagi perusahaan asuransi karena sudah terjadi. Klaim yang sudah terjadi namun belum dilaporkan ini disebabkan oleh keterlambatan atau disebut lag/jarak yang disebabkan oleh berbagai faktor. Setiap produk asuransi memiliki lag yang berbeda-beda. Perusahaan asuransi tidak mempunyai data keterlambatan tersebut sehingga data tersebut dapat dibentuk dari data klaim historis menggunakan run-off triangle. Tujuan dari run-off triangle adalah mengetahui berapa lama yang dibutuhkan dari suatu klaim yang terjadi sampai klaim tersebut dilaporkan. Data klaim historis dalam bentuk run-off triangle disebut sebagai incurred sehingga diperoleh gambaran pengalaman klaim dan data tersebut digunakan untuk mengestimasikan masa depan dengan tujuan untuk mendapatkan estimasi ultimate loss. Estimasi ultimate loss adalah estimasi total klaim jika sudah full terlaporkan. Jika sudah didapatkan estimasi ultimate loss dan incurred, maka selisihnya merupakan cadangan klaim yang sudah terjadi namum belum dilaporkan atau IBNR. Terdapat banyak metode untuk memperhitungkan cadangan klaim IBNR. Beberapa Metode yang dapat digunakan adalah dengan metode Chain-Ladder dan Bornhuetter-Ferguson. Hasil menunjukkan bahwa metode Bornhuetter-Ferguson lebih sesuai pada pehitungan cadangan klaim untuk produk indemnity di PT. XYZ. Hal ini disebabkan oleh data klaim historis di penelitian ini memiliki rata-rata waktu penundaan pelaporan klaim lebih dari dua hingga tiga bulan serta estimasi cadangan klaim dengan metode Bornhuetter-Ferguson menghasilkan cadangan klaim lebih besar dibandingkan dengan metode Chain-Ladder. Oleh karena itu, PT. XYZ akan lebih aman untuk menghindar risiko kekurangan cadangan jika menerapkan metode Bornhuetter-Ferguson dibandingkan dengan metode Chain-Ladder.

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5

Joubert, Morne, Tanja Verster, and Helgard Raubenheimer. "Default weighted survival analysis to directly model loss given default." South African Statistical Journal 52, no. 2 (2018): 173–202. http://dx.doi.org/10.37920/sasj.2018.52.2.5.

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Traditionally when predicting loss given default (LGD), the following models can be used: beta regression, inverse beta model, fractional response regression, ordinary least squares regression, survival analysis, run-off triangles and Box–Cox transformation. The run-off triangle method is commonly used in practice. When using survival analysis to model LGD a standard method to use is exposure at default (EAD) weighted survival analysis (denoted by EWSA). This article will aim to enhance the survival analysis estimation of LGD. Firstly by using default weighted LGD estimates and incorporating negative cash flows and secondly catering for over-recoveries. We will denote this new method to predict LGD as the default weighted survival analysis (DWSA). These enhancements were motivated by the fact that the South African Reserve Bank requires banks to use default weight LGD estimates in regulatory capital calculations. Therefore by including this into the survival analysis approach, the model is aligned more closely to regulations. Recovery datasets used by banks include both negative and over-recoveries. By including these into the LGD estimation, the models more are closely aligned to the actual data. The assumption is that the predictive power of the model should therefore be improved by adding these changes. The proposed model is tested on eight datasets. Three of these are actual retail bank datasets and five are simulated. The datasets used are representative of the data typically used in LGD estimations in the South African retail environment. This article will show that the proposed DWSA model outperforms the EWSA model by resulting in not only the lowest mean squared error (MSE), but also the lowest bias and variance across all eight datasets. Furthermore, the DWSA model outperforms all other models under review.

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6

Lee, Sungim, and Johan Lim. "Online estimation of the case fatality rate using a run‐off triangle data approach: An application to the Korean MERS outbreak in 2015." Statistics in Medicine 38, no. 14 (March 5, 2019): 2664–79. http://dx.doi.org/10.1002/sim.8125.

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7

Kartikasari, Mujiati Dwi, and Hani’atul Maghfuroh. "Prediction of Outstanding Claims Liability in Non-Life Insurance: An Application of Adaptive Grey Model." EKSAKTA: Journal of Sciences and Data Analysis 2, no. 2 (September 17, 2021): 109–15. http://dx.doi.org/10.20885/eksakta.vol2.iss1.art13.

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In order to assess the solvency of non-life insurance companies, the prediction of outstanding claims liability is very important. Prediction of outstanding claims liability is usually done by using a run-off triangle data scheme. However, if data are not available to form the scheme, the prediction of outstanding claims liability cannot be made. Another alternative for predicting of outstanding claims liability is to use time series analysis. This research uses an adaptive grey model that has the advantage of being free of assumptions of data patterns and a minimum amount of data used to predict is small (at least 4 data). To determine the accuracy of the adaptive grey model, we compare the prediction of outstanding claims liability using a grey model classic. Based on the analysis results, the adaptive grey model is better than the classic gray model in predicting outstanding claims liability.

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8

Clemente, Gian Paolo, Nino Savelli, and Diego Zappa. "Modelling Outstanding Claims with Mixed Compound Processes in Insurance." International Business Research 12, no. 3 (February 13, 2019): 123. http://dx.doi.org/10.5539/ibr.v12n3p123.

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In general insurance, measuring the uncertainty of future loss payments and estimating the claims reserve are primary goals of actuaries. To deal with these tricky tasks, a broad literature is available on deterministic and stochastic approaches, most of which aims at straightforwardly modelling the overall claims reserve. In this paper by an extended, very general and reproducible case-study, we analyze the reserving process by attributing to each cell of the lower part of the run-off triangle a Compound mixed Poisson Process, calibrated upon both the numbers of claims and future average costs and considering as well the dependence among incremental claims. We provide analytically the moments of both incremental payments and the total reserve. Furthermore, we accordingly consider the probability distribution of the claims reserve, which is necessary for the assessment of the Risk Reserve capital requirement in a Solvency II framework. To test the impact of the model under different scenarios, insurers and lines of business, the case study is thoroughly analyzed by exploiting the Fisher-Lange average cost method.

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9

Zhang, Jiayi Eris, Jèrèmie Dumas, Yun (Raymond) Fei, Alec Jacobson, Doug L. James, and Danny M. Kaufman. "Progressive Simulation for Cloth Quasistatics." ACM Transactions on Graphics 41, no. 6 (November 30, 2022): 1–16. http://dx.doi.org/10.1145/3550454.3555510.

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The trade-off between speed and fidelity in cloth simulation is a fundamental computational problem in computer graphics and computational design. Coarse cloth models provide the interactive performance required by designers, but they can not be simulated at higher resolutions ("up-resed") without introducing simulation artifacts and/or unpredicted outcomes, such as different folds, wrinkles and drapes. But how can a coarse simulation predict the result of an unconstrained, high-resolution simulation that has not yet been run? We propose Progressive Cloth Simulation (PCS), a new forward simulation method for efficient preview of cloth quasistatics on exceedingly coarse triangle meshes with consistent and progressive improvement over a hierarchy of increasingly higher-resolution models. PCS provides an efficient coarse previewing simulation method that predicts the coarse-scale folds and wrinkles that will be generated by a corresponding converged, high-fidelity C-IPC simulation of the cloth drape's equilibrium. For each preview PCS can generate an increasing-resolution sequence of consistent models that progress towards this converged solution. This successive improvement can then be interrupted at any point, for example, whenever design parameters are updated. PCS then ensures feasibility at all resolutions, so that predicted solutions remain intersection-free and capture the complex folding and buckling behaviors of frictionally contacting cloth.

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10

Schmidt, Klaus D. "Loss prediction based on run-off triangles." AStA Advances in Statistical Analysis 96, no. 2 (December 7, 2011): 265–310. http://dx.doi.org/10.1007/s10182-011-0183-0.

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11

Merz, Michael, Mario V. Wüthrich, and Enkelejd Hashorva. "Dependence modelling in multivariate claims run-off triangles." Annals of Actuarial Science 7, no. 1 (September 5, 2012): 3–25. http://dx.doi.org/10.1017/s1748499512000140.

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AbstractA central issue in claims reserving is the modelling of appropriate dependence structures. Most classical models cannot cope with this task. We define a multivariate log-normal model that allows to model both, dependence between different sub-portfolios and dependence within sub-portfolios such as claims inflation. In this model we derive closed form solutions for claims reserves and the corresponding prediction uncertainty.

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12

Badounas, Ioannis, and Georgios Pitselis. "Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model." Risks 8, no. 1 (February 3, 2020): 14. http://dx.doi.org/10.3390/risks8010014.

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In this paper, we consider a loss reserving model for a general insurance portfolio consisting of a number of correlated run-off triangles that can be embedded within the quantile regression model for longitudinal data. The model proposes a combination of the between- and within-subportfolios (run-off triangles) estimating functions for regression parameter estimation, which take into account the correlation and variation of the run-off triangles. The proposed method is robust to the error correlation structure, improves the efficiency of parameter estimators, and is useful for the estimation of the reserve risk margin and value at risk (VaR) in actuarial and finance applications.

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13

Kim, Byungwon, Seonghong Kim, Sungkyu Jung, Woncheol Jang, and Johan Lim. "Comments on “Online estimation of the case fatality rate using a run‐off triangle data approach: An application to the Korean MERS outbreak in 2015” by Sungim Lee and Johan Lim published in Statistics in Medicine (vol. 38, 2644‐2679, 2019)." Statistics in Medicine 41, no. 9 (April 11, 2022): 1728–32. http://dx.doi.org/10.1002/sim.9123.

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14

Braun, Christian. "The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles." ASTIN Bulletin 34, no. 02 (November 2004): 399–423. http://dx.doi.org/10.2143/ast.34.2.505150.

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It is shown how the distribution-free method of Mack (1993) can be extended in order to estimate the prediction error of the Chain Ladder method for a portfolio of several correlated run-off triangles.

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15

Braun, Christian. "The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles." ASTIN Bulletin 34, no. 2 (November 2004): 399–423. http://dx.doi.org/10.1017/s0515036100013751.

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It is shown how the distribution-free method of Mack (1993) can be extended in order to estimate the prediction error of the Chain Ladder method for a portfolio of several correlated run-off triangles.

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16

Peterson, Brennan, Michael Kwan, Fred Duewer, Andrew Reid, and Rhiannon Brooks. "Optimizing X-Ray Inspection for Advanced Packaging Applications." International Symposium on Microelectronics 2020, no. 1 (September 1, 2020): 000165–68. http://dx.doi.org/10.4071/2380-4505-2020.1.000165.

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ABSTRACT Over the coming decade, advanced packaging will become increasingly critical to performance, cost, and density improvements in advanced electronics. There is both an industry push: cost and performance advances in transistor scaling are increasingly difficult. And there is an industry pull: customization for each market can be done far more quickly by assembling a series of parts in a package, rather than by design and integration into a single device. This isnt a new idea: Gordon Moore said the same in the 60’s. But after decades of increased device level integration, it is an important change. Figure 1 shows an example (future) device: there are large bumps, hybrid bonds--for extreme bandwidth and low latency connection to cache memory, TSV based DRAM, and multiple CPU to CPU interconnects. Each of these is a failure point. Figure 1: The wide variety of interconnects on future advanced packages Figure 2: the triangle of misery as applied to standard and Advanced xray imaging (AXI) Manufacturing will necessarily advance in the packaging arena: pin density and package size will both increase to support the high bandwidth and device integration demands. The downside of multiple device integration is a higher set of requirements on the reliability of both the individual devices and the fully assembled system. This is an opportunity to take advantage of new strategies and technologies in package inspection. The sampling challenges for both control and inspection for high reliability require systems that can run at 100% coverage and millions of units per year. An overview of reliability sampling challenges as it relates to the end of line inspection, as well as sampling for both defect type and incidence is critical to understanding how and what to measure to maximize yield. There are fundamental tradeoffs between speed, resolution, and signal to noise ratio that inform a systematic engineering understanding of inspection. Optimizing that trade-off specifically for semiconductor inspection leads to dedicated tools with extremely high resolution, speed, and low dose. In parallel with the speed requirements, sensitivity, and noise immunity can be improved with an understanding of the systematic sources of noise. These can be mitigated and even eliminated with novel algorithms for both image enhancement and defect location.

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17

Merz, M., and M. V. Wüthrich. "Prediction Error of the Chain Ladder Reserving Method applied to Correlated Run-off Triangles." Annals of Actuarial Science 2, no. 1 (March 2007): 25–50. http://dx.doi.org/10.1017/s1748499500000245.

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ABSTRACTIn Buchwalder et al. (2006) we revisited Mack's (1993) and Murphy's (1994) estimates for the mean square error of prediction (MSEP) of the chain ladder claims reserving method. This was done using a time series model for the chain ladder method. In this paper we extend the time series model to determine an estimate for the MSEP of a portfolio of N correlated run-off triangles. This estimate differs in the special case N = 2 from the estimate given by Braun (2004). We discuss the differences between the estimates.

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18

Wüthrich, Mario V. "Claims Reserving Using Tweedie's Compound Poisson Model." ASTIN Bulletin 33, no. 02 (November 2003): 331–46. http://dx.doi.org/10.2143/ast.33.2.503696.

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We consider the problem of claims reserving and estimating run-off triangles. We generalize the gamma cell distributions model which leads to Tweedie's compound Poisson model. Choosing a suitable parametrization, we estimate the parameters of our model within the framework of generalized linear models (see Jørgensen-de Souza [2] and Smyth-Jørgensen [8]). We show that these methods lead to reasonable estimates of the outstanding loss liabilities.

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19

Verrall, R. J., and Z. Li. "Negative incremental claims: chain ladder and linear models." Journal of the Institute of Actuaries 120, no. 1 (1993): 171–83. http://dx.doi.org/10.1017/s0020268100036891.

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AbstractThis paper considers the application of loglinear models to claims run-off triangles which contain negative incremental claims. Maximum likelihood estimation is applied using the three parameter lognormal distribution. The method can be used in conjunction with any model which can be expressed in lognormal form. In particular the chain ladder technique is considered. An example is given and the results compared with the basic actuarial method.

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20

Wüthrich, Mario V. "Claims Reserving Using Tweedie's Compound Poisson Model." ASTIN Bulletin 33, no. 2 (November 2003): 331–46. http://dx.doi.org/10.1017/s0515036100013490.

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We consider the problem of claims reserving and estimating run-off triangles. We generalize the gamma cell distributions model which leads to Tweedie's compound Poisson model. Choosing a suitable parametrization, we estimate the parameters of our model within the framework of generalized linear models (see Jørgensen-de Souza [2] and Smyth-Jørgensen [8]). We show that these methods lead to reasonable estimates of the outstanding loss liabilities.

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21

Peremans, Kris, Stefan Van Aelst, and Tim Verdonck. "A Robust General Multivariate Chain Ladder Method." Risks 6, no. 4 (September 30, 2018): 108. http://dx.doi.org/10.3390/risks6040108.

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The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) do not need to be equal to the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue, we propose a robust alternative that estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to automatically flag the claims with a significantly large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data.

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22

Raço, Endri ,., Kleida ,. Haxhi, Etleva Llagami, and Oriana Zaçaj. "Comparison of Statistical Methods for Claims Reserve Estimation Using R Language." WSEAS TRANSACTIONS ON MATHEMATICS 21 (July 14, 2022): 547–52. http://dx.doi.org/10.37394/23206.2022.21.61.

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Stochastic methods of reserves estimation serve to assess the technical provisions of outstanding claims and forecast cash payments of claims in the coming years. The chain ladder model developed by Mack is the more prevalent model. The main deﬁciency in the chain-ladder model is that the chain-ladder model depends on the last observation on the diagonal. If this last observation is an outlier, this outlier will be projected to the ultimate claim. One of the possibilities to smooth outliers on the last observed diagonal is to robustify such observations, making use of the maximum likelihood estimation along with the common Loss Development Factor (LDF) curve fitting and Cape Cod (CC) techniques. This paper aims to highlight the advantages of using these methods for the best estimate of claims reserves in the Domestic Motor Third Party Liability portfolio. The maximum–likelihood parameter estimation and Chi-square test, are used to specify the probability distribution that best fits the data. Using the Standard Chain Ladder method, LDF, and CC method the claims reserve is calculated based on the run-off triangles of paid claims or the run-off triangles of the incurred claims. Many times, the projections based on the paid claims are different than the projections based on the incurred claims. The solution for this problem is the Munich Chain Ladder method.

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23

Meng, Shengwang, and Guangyuan Gao. "COMPOUND POISSON CLAIMS RESERVING MODELS: EXTENSIONS AND INFERENCE." ASTIN Bulletin 48, no. 3 (May 11, 2018): 1137–56. http://dx.doi.org/10.1017/asb.2018.12.

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AbstractWe consider compound Poisson claims reserving models applied to the paid claims and to the number of payments run-off triangles. We extend the standard Poisson-gamma assumption to account for over-dispersion in the payment counts and to account for various mean and variance structures in the individual payments. Two generalized linear models are applied consecutively to predict the unpaid claims. A bootstrap is used to estimate the mean squared error of prediction and to simulate the predictive distribution of the unpaid claims. We show that the extended compound Poisson models make reasonable predictions of the unpaid claims.

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24

Lindholm, Mathias, Filip Lindskog, and Felix Wahl. "Estimation of conditional mean squared error of prediction for claims reserving." Annals of Actuarial Science 14, no. 1 (June 14, 2019): 93–128. http://dx.doi.org/10.1017/s174849951900006x.

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AbstractThis paper studies estimation of the conditional mean squared error of prediction, conditional on what is known at the time of prediction. The particular problem considered is the assessment of actuarial reserving methods given data in the form of run-off triangles (trapezoids), where the use of prediction assessment based on out-of-sample performance is not an option. The prediction assessment principle advocated here can be viewed as a generalisation of Akaike’s final prediction error. A direct application of this simple principle in the setting of a data-generating process given in terms of a sequence of general linear models yields an estimator of the conditional mean squared error of prediction that can be computed explicitly for a wide range of models within this model class. Mack’s distribution-free chain ladder model and the corresponding estimator of the prediction error for the ultimate claim amount are shown to be a special case. It is demonstrated that the prediction assessment principle easily applies to quite different data-generating processes and results in estimators that have been studied in the literature.

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25

Chen, Xuemei, Zhonghua Wei, Xia Zhao, Mingyang Hao, and Tongyang Zhang. "Conspicuity Research on the Highway Roadside Objects: A Simulator Study." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/864791.

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In a monotonous travelling environment, the single-vehicle run-off-roadside accidents occur easily. The injuries and fatalities caused by those accidents are significant components of the annual road casualties. The causation is the complex interaction of the visual effects on the roadside objects’ conspicuity. So the conspicuity enhancement needs to be considered in the roadside objects design to provide a temporary restoration of alertness and vigilance to drivers. Factors contributing to the conspicuity of the roadside objects were analyzed in this paper. A driving simulator study was conducted in order to extrapolate the relationship between the legibility distances and the objects and to quantify the conspicuity of the roadside objects different in basic features. The conclusions of this paper were firstly, a significant correlation existed between the mean legibility distance and the object’s size. The mean legibility distance was in a significant exponential proportion to the object’s size. Secondly, the triangle’s legibility was better than that of the rectangle and round contours. Only when the roadside object was combined with the suitable contour and size did the best visual quality come. To some extent, the conclusions could provide theoretical tools and strategies to optimize the dimensional design of the roadside objects in order to maintain the roadside safety.

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26

Mack, Thomas. "A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves." ASTIN Bulletin 21, no. 1 (April 1991): 93–109. http://dx.doi.org/10.2143/ast.21.1.2005403.

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AbstractIt is shown that there is a connection between rating in automobile insurance and the estimation of IBNR claims amounts because automobile insurance tariffs are mostly cross-classified by at least two variables (e.g. territory and driver class) and IBNR claims run-off triangles are always cross-classified by the two variables accident year and development year. Therefore, by translating the most well-known automobile rating methods into the claims reserving situation, some known and some unknown claims reserving methods are obtained. For instance, the automobile rating method of Bailey and Simon produces a new claims reserving method, whereas the model leading to the rating method called “marginal totals” produces the well-known IBNR claims estimation method called “chain ladder”. A drawback of this model is the fact that it is designed for the number of claims and not for the total claims amount for which it is usually applied.As an alternative for both, rating and claims reserving, we describe a simple but realistic parametric model for the total claims amount which is based on the Gamma distribution and has the advantage of providing the possibility of assessing the goodness-of-fit and calculating the estimation error. This method is not very well known in automobile insurance—although a satisfactory application is reported—and seems to be completely unknown in the field of claims reserving, although its execution is nearly as simple as that of the chain ladder method.

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27

Nieto-Barajas, Luis E., and Rodrigo S. Targino. "A GAMMA MOVING AVERAGE PROCESS FOR MODELLING DEPENDENCE ACROSS DEVELOPMENT YEARS IN RUN-OFF TRIANGLES." ASTIN Bulletin, November 4, 2020, 1–22. http://dx.doi.org/10.1017/asb.2020.36.

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ABSTRACT We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

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28

Kartikasari, Mujiati Dwi, and Hani’atul Maghfuroh. "Prediction of Outstanding Claims Liability in Non-Life Insurance: An Application of Adaptive Grey Model." EKSAKTA: Journal of Sciences and Data Analysis, September 17, 2021, 109–15. http://dx.doi.org/10.20885/eksakta.vol2.iss2.art4.

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In order to assess the solvency of non-life insurance companies, the prediction of outstanding claims liability is very important. Prediction of outstanding claims liability is usually done by using a run-off triangle data scheme. However, if data are not available to form the scheme, the prediction of outstanding claims liability cannot be made. Another alternative for predicting of outstanding claims liability is to use time series analysis. This research uses an adaptive grey model that has the advantage of being free of assumptions of data patterns and a minimum amount of data used to predict is small (at least 4 data). To determine the accuracy of the adaptive grey model, we compare the prediction of outstanding claims liability using a grey model classic. Based on the analysis results, the adaptive grey model is better than the classic gray model in predicting outstanding claims liability.

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29

Merz, Michael, Mario V. Wuthrich, and Enkelejd Hashorva. "Dependence Modeling in Multivariate Claims Run-Off Triangles." SSRN Electronic Journal, 2011. http://dx.doi.org/10.2139/ssrn.1975336.

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30

Delong, Lukasz, and Marcin Szatkowski. "One-Year and Ultimate Correlations in Dependent Claims Run-Off Triangles." SSRN Electronic Journal, 2022. http://dx.doi.org/10.2139/ssrn.4220253.

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Xie, Jia-Ming, Xi-Zhe Ling, Ming-Zhu Liu, and Li-Sheng Geng. "Search for hidden-charm pentaquark states in three-body final states." European Physical Journal C 82, no. 11 (November 24, 2022). http://dx.doi.org/10.1140/epjc/s10052-022-11026-0.

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AbstractThe three pentaquark states, $$P_c(4312)$$ P c ( 4312 ) , $$P_c(4440)$$ P c ( 4440 ) and $$P_c(4457)$$ P c ( 4457 ) , discovered by the LHCb Collaboration in 2019, are often interpreted as $${\bar{D}}^{(*)}\Sigma _c$$ D ¯ ( ∗ ) Σ c molecules. Together with their four $${\bar{D}}^{(*)}\Sigma _{c}^{*}$$ D ¯ ( ∗ ) Σ c ∗ partners dictated by heavy quark spin symmetry they represent a complete multiplet of hadronic molecules of $${\bar{D}}^{(*)}\Sigma _{c}^{(*)}$$ D ¯ ( ∗ ) Σ c ( ∗ ) . The pentaquark states were observed in the $$J/\psi p$$ J / ψ p invariant mass distributions of the $$\Lambda _b\rightarrow J/\psi p K$$ Λ b → J / ψ p K decay. It is widely recognized that to understand their nature, other discovery channels play an important role. In this work, we investigate two three-body decay modes of the $${\bar{D}}^{(*)}\Sigma _{c}^{(*)}$$ D ¯ ( ∗ ) Σ c ( ∗ ) molecules. The tree-level modes proceed via off-shell $$\Sigma _{c}^{(*)}$$ Σ c ( ∗ ) baryons, $${\bar{D}}^{(*)}\Sigma _{c}^{(*)} \rightarrow {\bar{D}}^{(*)}\left( \Sigma _{c}^{(*)}\rightarrow \Lambda _{c}\pi \right) \rightarrow {\bar{D}}^{(*)}\Lambda _{c}\pi $$ D ¯ ( ∗ ) Σ c ( ∗ ) → D ¯ ( ∗ ) Σ c ( ∗ ) → Λ c π → D ¯ ( ∗ ) Λ c π , while the triangle-loop modes proceed through $${\bar{D}}^{*}\Sigma _{c}^{(*)}\rightarrow J/\psi N\pi $$ D ¯ ∗ Σ c ( ∗ ) → J / ψ N π , $$\eta _{c}N\pi $$ η c N π via $${\bar{D}}\Sigma _{c}^{(*)}$$ D ¯ Σ c ( ∗ ) rescattering to $$J/\psi N$$ J / ψ N and $$\eta _{c}N$$ η c N . Our results indicate that the decay widths of the $$P_{c}(4457)$$ P c ( 4457 ) and $${\bar{D}}^{(*)}\Sigma _{c}^{*}$$ D ¯ ( ∗ ) Σ c ∗ states into $${\bar{D}}^{(*)}\Lambda _{c}\pi $$ D ¯ ( ∗ ) Λ c π are several MeV, as a result can be observed in the upcoming Run 3 and Run 4 of LHC. The partial decay widths into $${\bar{D}}^{(*)}\Lambda _{c}\pi $$ D ¯ ( ∗ ) Λ c π of the $$P_{c}(4312)$$ P c ( 4312 ) and $$P_{c}(4440)$$ P c ( 4440 ) states range from tens to hundreds of keV. In addition, the partial decay widths of $${\bar{D}}^{*}\Sigma _{c}$$ D ¯ ∗ Σ c molecules into $$J/\psi N \pi $$ J / ψ N π and $$\eta _c N \pi $$ η c N π are several keV and tens of keV, respectively, and the partial decay widths of $${\bar{D}}^{*}\Sigma _{c}^{*}$$ D ¯ ∗ Σ c ∗ molecules into $$J/\psi N \pi $$ J / ψ N π vary from several keV to tens of keV. In particular, we show that the spin-5/2 $${\bar{D}}^{*}\Sigma _{c}^{*}$$ D ¯ ∗ Σ c ∗ state can be searched for in the $$J/\psi N \pi $$ J / ψ N π and $${\bar{D}}^{*}\Lambda _{c}\pi $$ D ¯ ∗ Λ c π invariant mass distributions, while the latter one is more favorable. These three-body decay modes of the pentaquark states are of great value to further observations of the pentaquark states and to a better understanding of their nature.

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Maciak, Matúš, Ivan Mizera, and Michal Pešta. "FUNCTIONAL PROFILE TECHNIQUES FOR CLAIMS RESERVING." ASTIN Bulletin, March 10, 2022, 1–34. http://dx.doi.org/10.1017/asb.2022.4.

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Abstract One of the most fundamental tasks in non-life insurance, done on regular basis, is risk reserving assessment analysis, which amounts to predict stochastically the overall loss reserves to cover possible claims. The most common reserving methods are based on different parametric approaches using aggregated data structured in the run-off triangles. In this paper, we propose a rather non-parametric approach, which handles the underlying loss development triangles as functional profiles and predicts the claim reserve distribution through permutation bootstrap. Three competitive functional-based reserving techniques, each with slightly different scope, are presented; their theoretical and practical advantages – in particular, effortless implementation, robustness against outliers, and wide-range applicability – are discussed. Theoretical justifications of the methods are derived as well. An evaluation of the empirical performance of the designed methods and a full-scale comparison with standard (parametric) reserving techniques are carried on several hundreds of real run-off triangles against the known real loss outcomes. An important objective of the paper is also to promote the idea of natural usefulness of the functional reserving methods among the reserving practitioners.

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Hendrych, Radek, and Tomas Cipra. "APPLYING STATE SPACE MODELS TO STOCHASTIC CLAIMS RESERVING." ASTIN Bulletin, November 24, 2020, 1–35. http://dx.doi.org/10.1017/asb.2020.38.

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Abstract The paper solves the loss reserving problem using Kalman recursions in linear statespace models. In particular, if one orders claims data from run-off triangles to time series with missing observations, then state space formulation can be applied for projections or interpolations of IBNR (Incurred But Not Reported) reserves. Namely, outputs of the corresponding Kalman recursion algorithms for missing or future observations can be taken as the IBNR projections. In particular, by means of such recursive procedures one can perform effectively simulations in order to estimate numerically the distribution of IBNR claims which may be very useful in terms of setting and/or monitoring of prudency level of loss reserves. Moreover, one can generalize this approach to the multivariate case of several dependent run-off triangles for correlated business lines and the outliers in claims data can be also treated effectively in this way. Results of a numerical study for several sets of claims data (univariate and multivariate ones) are presented.

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Usman, Farha, and Jennifer S. K. Chan. "NEW LOSS RESERVE MODELS WITH PERSISTENCE EFFECTS TO FORECAST TRAPEZOIDAL LOSSES IN RUN-OFF TRIANGLES." ASTIN Bulletin, September 21, 2022, 1–44. http://dx.doi.org/10.1017/asb.2022.17.

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Abstract Modelling loss reserve data in run-off triangles is challenging due to the complex but unknown dynamics in the claim/loss process. Popular loss reserve models describe the mean process through development year, accident year, and calendar year effects using the analysis of variance and covariance (ANCOVA) models. We propose to include in the mean function the persistence terms in the conditional autoregressive range model for modelling the persistence of claim across development years. In the ANCOVA model, we adopt linear trends for the accident and calendar year effects and a quadratic trend for the development year effect. We investigate linear or log-transformed mean functions and four distributions, namely generalised beta type 2, generalised gamma, Weibull, and exponential extension, with positive support to enhance the model flexibility. The proposed models are implemented using the Bayesian user-friendly package Stan running in the R environment. Results show that the models with log-transformed mean function and persistence terms provide better model fits. Lastly, the best model is applied to forecast partial loss reserve and calendar year reserve for three years.

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35

Feisst, Debbie. "The Rising by K. Armstrong." Deakin Review of Children's Literature 3, no. 1 (July 9, 2013). http://dx.doi.org/10.20361/g2ck5t.

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Armstrong, Kelley. The Rising. Toronto: HarperTeen, 2013. Print. Ontario-based award-winning writer Kelley Armstrong, author of the New York Times and Globe and Mail bestselling Darkest Powers young adult urban fantasy trilogy, brings us the third and final title of her Darkness Rising trilogy. The first in the trilogy, 2011’s The Gathering, was previously reviewed in the inaugural issue of Deakin, Vol. 1 No 1 and the second, The Calling, was reviewed in Vol. 2 No. 4. As with the previous book in the trilogy, this book is not meant to be read on its own, as again the author’s recap on events and characters is minimal. I felt the need to revisit the second book and familiarize myself with the plot before I started in on The Rising as it had been a year between books, the price of being a fan of series fiction. Sixteen-year-old supernatural, Maya Delaney, and her fellow supe friends are assumed dead after an apparent helicopter rescue-turned-crash leaves them running for their lives. With no one they can trust to turn to, the teens are truly in harm’s way as their supernatural abilities start careening out of control. Corey’s headaches are increasing, Nicole’s mental state is fragile at best and even Maya is concerned that she herself may be regressing. Like it or not, the friends need assistance from the rival networks that seek to exploit their abilities. Maya’s biological father, Calvin Antone, plays a larger role in this book and again, his intentions are often unclear. The intensifying romance of the previous book does indeed lead to the expected supernatural YA love triangle, but it feels forced and formulaic, as if the author’s fans would expect it and so it was hastily written in. There is a continued lack of storyline that seems to centre around the characters’ need to run and hide, which is echoed in Armstrong’s other works. I am giving this book three stars out of four because true Armstrong fans will enjoy the series as a whole as well as the tie-in to well-loved characters in her Darkest Powers trilogy and devour it regardless of its limitations. The epilogue will be particularly satisfying. I would not be surprised to learn of yet another spin-off series with Maya or some of the new characters introduced in the series. Recommended: 3 out of 4 stars Reviewer: Debbie Feisst Debbie is a Public Services Librarian at the H.T. Coutts Education Library at the University of Alberta. When not renovating, she enjoys travel, fitness and young adult fiction.

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Heberle, Jochen, Luis Huergo, and Michael Merz. "Bootstrapping the Chain-Ladder Method for Correlated Run-Off-Triangles for Achieving the Predictive DIstribution of the Claims Development Result." SSRN Electronic Journal, 2011. http://dx.doi.org/10.2139/ssrn.2060361.

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