Riskcenter
The research group on Risk in Insurance and Finance is attached to the Institute of Applied Economics IREA-UB
Barcelona Insurance and Risk Management Summer School 2012
SGR 2009-1328
Consolidated research group
Advances in Panel Data for Acuarial Applications. July 16-18.
Abstract
In this talk, we survey a
collection of work about the use of modern statistical
techniques for actuarial applications. In particular, we
cover:
- use of micro-level data for macro-eff ects inference
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" eff ect of
claim counts experience of a pool of insurers.
- risk classi cation in insurance
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
tari ff associated with these risks. An important part of
the process of establishing fair insurance tari ffs 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.
- longitudinal data analysis and predictive modeling
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 e ffect 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 e ffects 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.
About the speaker
Emiliano
(Emil) A. Valdez, Ph.D, FSA, is a Professor of
Actuarial Science in the Department of Mathematics at
the University of Connecticut, USA. He is a Fellow of
the Society of Actuaries and holds a Ph.D. from the
University of Wisconsin in Madison. His academic
experience includes several years of teaching and
conducting research in actuarial science in three
di erent continents: North America, Australia and
Asia. His previous academic posts include working for
the Nanyang Business School in Singapore and for the
University of New South Wales in Sydney, Australia. He
has been awarded the Edward A. Lew Award, the Halmstad
Memorial Prize, and recently in 2010, the Charles A.
Hachemeister Prize, in recognition for his signi cant
contributions to the actuarial literature. His current
research interest includes copula models and
dependencies, managing post-retirement assets, and
risk measures and capital requirements related to
enterprise risk management. He also has several years
of industry experience working as an actuary for
Connecticut Mutual in Hartford and held summer
actuarial positions at Price Waterhouse.
References
- 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.
Course schedule
Day 1: Monday July 16 10-14
Day 2: Tuesday July 17 10-14
Day 3: Wednesday July 18 10-14