In this talk, we survey a collection of work about the use of modern statistical techniques for actuarial applications. In particular, we cover:

Data at the individual policy level that are tracked over time, which we call micro-data, have the potential to reveal unsuspected patterns of behavior and to allow the analyst to develop new financing mechanisms to manage risks. We describe various modeling frameworks that are calibrated using a database of individual automobile insurance policies. Outcomes are potentially multivariate, a mixture of zeros, and continuous claims, and when continuous, have long-tail distributions. In yet a different framework, we use multilevel models to analyze the "intercompany" effect of claim counts experience of a pool of insurers.

Actuaries are considered professional experts in the economic assessment of uncertain events, and equipped with many statistical tools for analytics, they help formulate a fair and reasonable tariff associated with these risks. An important part of the process of establishing fair insurance tariffs is risk classication, which involves the grouping of risks into various classes that share a homogeneous set of characteristics allowing the actuary to reasonably price discriminate. We survey some of the statistical tools for risk classiffication used in insurance. We also distinguish between "a priori" and "a posteriori" ratemaking. The former is a process which forms the basis for ratemaking when a policyholder is new and insufficient information may be available. The latter process uses additional historical information about policyholder claims when this becomes available.

We explore the usefulness of copulas to model the number of insurance claims for an individual policyholder within a longitudinal context. To address the limitations of copulas commonly attributed to multivariate discrete data, we adopt a "jittering" method to the claim counts which has the effect of continuitizing the data. Elliptical copulas are proposed to accommodate the intertemporal nature of the "jittered" claim counts and the unobservable subject-specific heterogeneity on the frequency of claims. Observable subject-specific effects are accounted in the model by using available covariate information through a regression model. The predictive distribution together with the corresponding credibility of claim frequency can be derived from the model for ratemaking and risk classication purposes. 

• Frees and Valdez (2008), Hierarchical Insurance Claims Modeling, Journal of the American Statistical Association, Vol. 103, No. 484, pp. 1457-1469.
• Frees, Shi and Valdez (2009), Actuarial Applications of a Hierarchical Insurance Claims Model, ASTIN Bulletin, Vol. 39, No. 1, pp. 165-197.
• Young, Valdez and Kohn (2009), Multivariate Probit Models for Conditional Claim Types, Insurance: Mathematics and Economics, Vol. 44, No. 2, pp. 214-228.
• Antonio, Frees and Valdez (2010), A Multilevel Analysis of Intercompany Claim Counts, ASTIN Bulletin,Vol. 40, No. 1, pp. 151-177.
• Antonio, Frees and Valdez (2009), A Hierarchical Model for Micro-Level Stochastic Loss Reserving, work in progress.
• Antonio and Valdez (2011), Statistical Concepts of a priori and a posteriori Risk Classication in Insurance, AsTA, Advances in Statistical Analysis, forthcoming.
• Shi and Valdez (2012), Longitudinal Modeling of Insurance Claim Counts using Jitters, Scandinavian Actuarial Journal, forthcoming.