scholarly journals An Individual Claims Reserving Model

2007 ◽  
Vol 37 (01) ◽  
pp. 113-132 ◽  
Author(s):  
Keyword(s):  
Stochastic Models ◽  
Seasonal Effects ◽  
Claim Size ◽  
Unrealistic Assumption ◽  
Chain Ladder ◽  
The Individual ◽  
Ladder Models

Traditional Chain Ladder models are based on a few cells in an upper triangle and often give inaccurate projections of the reserve. Traditional stochastic models are based on the same few summaries and in addition are based on the often unrealistic assumption of independence between the aggregate incremental values. In this paper a set of stochastic models with weaker assumptions based on the individual claims development are described. These models can include information about settlement and can handle seasonal effects, changes in mix of business and claim types as well as changes in mix of claim size. It is demonstrated how the distribution of the process can be specified and especially how the distribution of the reserve can be determined. The method is illustrated with an example.

scholarly journals An Individual Claims Reserving Model

2007 ◽  
Vol 37 (1) ◽  
pp. 113-132 ◽  
Author(s):  
Keyword(s):  
Stochastic Models ◽  
Seasonal Effects ◽  
Claim Size ◽  
Unrealistic Assumption ◽  
Chain Ladder ◽  
The Individual ◽  
Ladder Models

Traditional Chain Ladder models are based on a few cells in an upper triangle and often give inaccurate projections of the reserve. Traditional stochastic models are based on the same few summaries and in addition are based on the often unrealistic assumption of independence between the aggregate incremental values. In this paper a set of stochastic models with weaker assumptions based on the individual claims development are described. These models can include information about settlement and can handle seasonal effects, changes in mix of business and claim types as well as changes in mix of claim size. It is demonstrated how the distribution of the process can be specified and especially how the distribution of the reserve can be determined. The method is illustrated with an example.

scholarly journals Parameter reduction in log-normal chain-ladder models

2015 ◽  
Vol 5 (2) ◽  
pp. 355-380 ◽  
Author(s):  
Richard J. Verrall ◽  
Mario V. Wüthrich
Keyword(s):  
Parameter Reduction ◽  
Chain Ladder ◽  
Log Normal ◽  
Ladder Models

scholarly journals A Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums

Risks ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 20
Author(s):  
Emilio Gómez-Déniz ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Risk Factors ◽  
Regression Model ◽  
Automobile Insurance ◽  
Claim Size ◽  
Insurance Portfolio ◽  
Different Types ◽  
Mixed Regression ◽  
The Individual ◽  
Size Threshold ◽  
Gender Type

In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and below a given claim size threshold in an automobile insurance portfolio. Relevant properties of this model are given. Next, a mixed regression model is derived to compute credibility bonus-malus premiums based on the individual claim size and other risk factors such as gender, type of vehicle, driving area, or age of the vehicle. Results are illustrated by using a well-known automobile insurance portfolio dataset.

BAYESIAN CHAIN LADDER MODELS

2014 ◽  
Vol 45 (1) ◽  
pp. 75-99 ◽  
Author(s):  
Greg Taylor
Keyword(s):  
Credibility Estimator ◽  
Implicit Equations ◽  
Special Cases ◽  
Recursive Formulas ◽  
Error Terms ◽  
Map Estimator ◽  
The Cross ◽  
Chain Ladder ◽  
Ladder Models ◽  
Linear Bayes

AbstractThe literature on Bayesian chain ladder models is surveyed. Both Mack and cross-classified forms of the chain ladder are considered. Both cases are examined in the context of error terms distributed according to a member of the exponential dispersion family. Tweedie and over-dispersed Poisson errors follow as special cases. Bayesian cross-classified chain ladder models may randomise row, column or diagonal parameters. Column and diagonal randomisation has been largely absent from the literature until recently. The present paper allows randomisation of row and column parameters. The Bayes estimator, the linear Bayes (credibility) estimator, and the MAP estimator are shown to be identical in the Mack case, and in the cross-classified case provided that the error terms are Tweedie distributed. In the Mack case the variance structure is generalised considerably from the existing literature. In the cross-classified case the model structure differs somewhat from the existing literature, and a comparison is made between the two. MAP estimators for the cross-classified case are often given by implicit equations that require numerical solution. Recursive formulas are given for these in the general case of error terms from the exponential dispersion family. The connection between the cross-classified case and Bornhuetter-Ferguson prediction is explored.

scholarly journals Deciphering landscape preferences: Investigating the roles of familiarity and biome types

2021 ◽  
Author(s):  
Giancarlo Mangone ◽  
Raelyne L Dopko ◽  
John M. Zelenski
Keyword(s):  
Temperate Forest ◽  
Seasonal Effects ◽  
Natural Environments ◽  
Substantial Variation ◽  
Methodological Choices ◽  
Nature Relatedness ◽  
Three Samples ◽  
Potential Applications ◽  
The Individual ◽  
Subjective Familiarity

Although people generally have positive evaluations of natural environments and stimuli, theory and research suggest that certain biomes are more preferable than others. Existing theories often draw on evolutionary ideas and people’s familiarity with biome types, with familiarity being the most supported, albeit not conclusively, in existing research. Across three samples (n = 720) we sought to compare preference ratings of 40 images that represented ten biomes (beach, lake, tropical and temperate forest, marsh, swamp, meadow, park, mountain, and river). We addressed objective familiarity by recruiting samples from two distinct geographies (Florida and Ontario), and we assessed subjective familiarity via image ratings. Familiarity was positively associated with liking biomes, though this trend was stronger for subjective familiarity compared to geography. Substantial variation in biome type preferences could not be attributed to familiarity. Specific biome types were strongly preferred irrespective of familiarity and geography. e.g., beaches and lakes were highly preferred, while marshes and swamps were substantially less preferred than other biome types. Further analyses found that the individual difference of nature relatedness predicted both familiarity and liking of all biomes except beaches, and that there was a lack of seasonal effects (fall and winter) across two Ontario samples. We discuss how results provide qualified support for the familiarity view, limits of this interpretation, how methodological choices such as the number of ratings might impact findings, and the potential applications of these results in landscape design.

Maternal aging affects life performance of progeny in a Holstein dairy cow model

2014 ◽  
Vol 5 (5) ◽  
pp. 374-384 ◽  
Author(s):  
S. Astiz ◽  
A. Gonzalez-Bulnes ◽  
F. Sebastian ◽  
O. Fargas ◽  
I. Cano ◽  
...  
Keyword(s):  
Cold Season ◽  
Protein Yield ◽  
Seasonal Effects ◽  
Management Guidelines ◽  
Optimal Health ◽  
Health And Disease ◽  
Fat Yield ◽  
The Individual ◽  
Holstein Dairy Cow ◽  
Maternal Aging

The development and life performance of 404 high-producing Holstein dairy cows was studied from birth onwards and during two lactations. The management, environment and parental genetics of the cows were known in detail. Cluster analysis identified four performance ‘types’: high-yielding (HY) cows and persistently high-yielding (PHY) cows, which accounted for 33% of the animals; medium-yielding (MY) cows, 41%; and low-yielding (LY) cows, 26%. Prenatal determinants of the life performance of the progeny were analyzed. Developmental and environmental factors were excluded as determinants of performance (including birth weight, level of passive immunity transfer, growth rate, age at first parturition and reproductive efficiency). Life performance did show minor seasonal effects, with more HY cows but less PHY being born during the cold season (90.1% in HY; 58.3% in PHY v. 81.5%). Instead, the single most important factor influencing life performance of daughters was maternal age. HY cows were born from the youngest mothers (1.89±1.14 parturitions, 3.12±1.42-year old), whereas LY cows were born from the oldest (2.72±1.80 parturitions, 3.97±2.01-year old; P<0.001). Life performance of the dams did not differ among clusters. In addition, metabolic parameters (fat and protein yield) were found to correlate significantly with yields between the first and second lactations (milk yield: r=0.357; fat yield: r=0.211; protein yield: r=0.277; P<0.0001), suggesting the influence of the individual. These results suggest that under optimal health, nutritional and environmental conditions, maternal aging is an important determinant of the life performance of progeny and argue for the need to identify conditions that contribute to health and disease in progeny according to the Developmental Origin of Health and Disease or DOHaD concept. Our findings may help the development of novel management guidelines for dairy farms.

EXISTENCE AND UNIQUENESS OF CHAIN LADDER SOLUTIONS

2016 ◽  
Vol 47 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Greg Taylor
Keyword(s):  
Maximum Likelihood ◽  
Existence And Uniqueness ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
The Cross ◽  
Chain Ladder ◽  
Ladder Models

AbstractThe cross-classified chain ladder has a number of versions, depending on the distribution to which observations are subject. The simplest case is that of Poisson distributed observations, and then maximum likelihood estimates of parameters are explicit. Most other cases, however, including Bayesian chain ladder models, lead to implicit MAP (Bayesian) or MLE (non-Bayesian) solutions for these parameter estimates, raising questions as to their existence and uniqueness. The present paper investigates these questions in the case where observations are distributed according to some member of the exponential dispersion family.

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