Description: In this paper, fuzzy sets - collections of objects whose boundaries are not precisely defined - are used to model the selection process in group health insurance. Both single and multiple options plans are discussed. Discussions of this paper are included.

Description: Under Yaari's dual theory of risk, this paper determines the equilibrium separating contracts for high and low risks in a competitive insurance market, in which risks are defined only by their expected losses, that is, a high risk is a risk that has a greater expected loss than a low risk. The authors also determine the pooling equilibrium contract when insurers are assumed non-myopic. Utility theory generally predicts that optimal insurance indemnity payments are nonlinear functions of the underlying loss due to the nonlinearity of agents' utility functions. Under Yaari's dual theory, the authors show that under mild technical conditions the indemnity payment is a piecewise linear function of the loss, a common property of insurance coverages.

Description: In performing Bayesian analysis of insurance losses, one usually chooses a parametric conditional loss distribution for each risk and a parametric prior distribution to describe how the conditional distributions vary across the risks. Young [1997] applies techniques from nonparametric density estimation to estimate the prior and uses the estimated model to calculate the predictive mean of future claims given past claims. A shortcoming of this method is that, in estimating the prior, one assumes the average claim amount equals the conditional mean. This is the abstract of a paper that considers a class of priors obtained by perturbing the one determined nonparametrically, as in Young [1997]. The authors thereby reflect the uncertainty in the prior that arises from the randomness in the claim data. They then calculate intervals for the corresponding predictive means. They illustrate their method with data from Dannenburg et. al. [1996] and compare the intervals of the predictive means with nonparametric confidence intervals.

Description: In this paper, the authors take an axiomatic approach to characterize insurance prices in a competitive market setting. Four axioms are presented to describe the behavior of market insurance prices. From these axioms it follows that the price of an insurance risk has a Choquet integral representation with respect to a distorted probability.

Description: Abstract for a paper that develops links between credibility theory in actuarial science and longitudinal data models in statistics. The paper demonstrates that many additive credibility models can be expressed as special cases of the longitudinal data model.