This dissertation introduces and develops sequential methods in actuarial science. In particular, it focuses on the assessment of credibility, estimation of credibility factors, and testing for full credibility based on sequentially collected actuarial data.;Actuaries routinely make decisions that are sequential in nature. During each insured period, the new claims and losses data are collected, and together with the new economic and financial situation and other factors, they are taken into account for the calculation of revised premiums and risks. For all the insureds, several decisions are made regularly, at least once per each insured period: whether the coverage should continue, whether the coverage should be changed and what premium should be charged.;To address the sequential nature of actuarial data collection and many actuarial decisions, the classical sequential methods and sequential ideas are applied to actuarial models. Specificity of actuarial data is contained in the frequency-severity model where the total consists of a random number of losses (frequency), each loss being also a random variable (severity).;As in classical sequential testing, during each insured period, the corresponding hypothesis can be either accepted or rejected, or sampling will continue. To derive this sequential test, asymptotic normality of the total loss is used along with the method of integrating out the nuisance parameters, as in the sequential t-test. Proposed tests control the error rate and power. They result in a rigorous set of conditions under which a cohort becomes fully credible.;Following sequential decisions, methods are developed for the computation of sequential P-values. P-values have a different meaning in sequential analysis, where test statistics obtained from samples of different sizes are compared. Inversion of the derived sequential test leads to a construction of a sequence of repeated confidence intervals (RCIs) for the credibility factor.;The real loss data are confidential, but the actuarial data generated by the Casualty Actuarial Society Public Loss Simulator are similar to the real data sets. Sequential methods proposed and developed in this dissertation are applied to the Public Loss Simulator data, and their performance is evaluated.
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