Credibility Models with Time-Varying Trend Components

Ledolter, Johannes; Klugman, Stuart A.; Lee, Chang‐Soo

doi:10.2143/ast.21.1.2005402

Cited by 32 publications

(5 citation statements)

References 18 publications

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“…For α 0 , ρ, and η we use standard normal N (0, 1) priors and for the precision (inverse variance) parameters σ and τ we use Gamma(a, b) priors. The literature provides empirical evidence to support the introduction of this model for describing loss ratios (Ledolter et al, 1991) and a simple plot of the data in Figure 1 confirms that the observed behaviour can be described by a model of this sort. However, one disadvantage of this model is that whereas the loss ratios are always non-negative, the normal model has support extending across the entire real line so that negative values could, in theory, occur.…”

Section: The Data and Modelsupporting

confidence: 55%

Bayesian Analysis of Loss Ratios Using the Reversible Jump Algorithm

Brown¹,

Brooks²

2011

Preprint

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Section: The Data and Modelsupporting

confidence: 55%

Bayesian Analysis of Loss Ratios Using the Reversible Jump Algorithm

Brown¹,

Brooks²

2011

Preprint

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“…We also assume the variance of any particular observation about its mean is proportional to some measure of the exposure. This assumption is popular among insurance practitioners such as Ledolter et al (1991), Klugman (1992), andRamlau-Hansen (1982). The second level comprising Equations ( 8) and ( 9), allows for any interaction between the class and occupation parameters α = (α 1 , .…”

Section: Short Review Of the Klugman Modelmentioning

confidence: 99%

Discrimination for two-way models with insurance applications

Brown¹,

Buckley

2013

Risk and Decision Analysis

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In this paper, we review and apply several approaches to model selection for analysis of variance models which are used in a credibility and insurance context. The reversible jump algorithm is employed for model selection, where posterior model probabilities are computed. We then apply this method to insurance data from workers' compensation insurance schemes. The reversible jump results are compared with the Deviance Information Criterion, and are shown to be consistent.For a general review of Bayesian modelling averaging, see Clyde (1999), andHoeting et al. (1999). However, when the set of candidate models M is not exhaustive, we might not be able to average over all possible models. In that context, placing a prior distribution on M does not apply, and since we are interested only in predicting future unknown values, this might be more appropriate than selecting a single model. The second alternative is the so called M -completed view, which simply seeks to compare a set of models which are available at that time. In this case M = {M i } simply constitute a range of specified models to be compared. From this perspective, assigning the probabilities {P(M i ), M i ∈ M } does not make sense and the actual overall model specifies beliefs for R of the form p(R) = p(R|M t ). Typically, {M i } will 2 have been proposed largely because they are attractive from the point of view of tractability of analysis or communication of results, compared with the actual belief model M t . The third alternative is the M -open view. In an M -open system it is assumed that none of the models being considered is the true model which generated the observations. In this case, our goal is to select some model or subset of models which best describe the data. For the M -completed and M -open views, assigning prior probabilities on the model space M is inappropriate since statements like p(M k ) = c do not make sense. However, in the M -open case, there is not separate overall belief specification.3 Decision Theoretic Approach Key et al. (1999) argue that any criteria for model comparison should depend on the decision context in which the comparison is taking place, as well as the perspective from which the models are viewed. In particular, an appropriate utility structure is required, making explicit those aspects of the performance of the model that is most important. Using a decision theoretic approach, we can assign utilities to the choice of model M i , u(M i , γ), where γ is some unknown of interest. The general decision problem is then to choose the optimal model, M * , by maximising expected utilitieswith π(γ|R) representing actual beliefs about γ after observing R in Equation (1). Spiegelhalter et al. (2002) propose their deviance information criterion, DIC, as an alternative to Bayes' factors. In Spiegelhalter et al. (2002), the DIC is developed to address how well the posterior might predict future data generated by the same mechanism that gave rise to the observed data. Our motivation is that likelihood ratio tests cannot be u...

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“…Another time effect to investigate is the change, or trend, in the number or amount of claims from year to year. Such work could follow the models given by KREMER (1982) or LEDOLTER, KLUGMAN and LEE (1991).…”

Section: Long-term Effectsmentioning

confidence: 99%

Credibility and Persistency

Young

1996

ASTIN Bull.

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Policyholders often decide to buy, renew, or cancel insurance based on the premium charged by the insurer compared with what they expect their claims will be. It is important for actuaries to consider the persistency of policyholders because the financial well-being of the insurer depends on spreading its risk over a large book of business. We use statistical decision theory to develop premium formulas that account for the past experience of a given policyholder, the experience of the entire collection of policyholders, and the likelihood of the policyholder renewing with or buying from a given insurer, that is, persistency.We assume that the persistency of policyholders depends on the arithmetic difference between the premium charged and their anticipated claims. We extend the work of TAYLOR (1975) in which he obtains linear credibility formulas by minimizing loss functions that incorporate the persistency of policyholders. We consider Taylor's loss functions and other objective functions, including those that account for the amount of business the insurer writes or renews.

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Credibility Models with Time-Varying Trend Components

Cited by 32 publications

References 18 publications

Bayesian Analysis of Loss Ratios Using the Reversible Jump Algorithm

Bayesian Analysis of Loss Ratios Using the Reversible Jump Algorithm

Discrimination for two-way models with insurance applications

Credibility and Persistency

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