Examination and Other Requirement
Details
Exam C (Construction and Evaluation of
Actuarial Models) The examination for this material consists of
four hours of multiple-choice questions and is identical to CAS
Exam 4. This material provides an introduction to modeling and
covers important actuarial methods that are useful in modeling. A
thorough knowledge of calculus, probability and mathematical
statistics is assumed. The candidate will be introduced to useful
frequency and severity models beyond those covered in Exam M. The
candidate will be required to understand the steps involved in the
modeling process and how to carry out these steps in solving
business problems. The candidate should be able to: - analyze data from an application in a business context;
- determine a suitable model including parameter values; and
- provide measures of confidence for decisions based upon the
model. The candidate will be introduced to a variety of tools for
the calibration and evaluation of the models.
A variety of tables will be provided to the
candidate in the study note package and at the examination. These
include values for the standard normal distribution, chi-square
distribution, and abridged inventories of discrete and continuous
probability distributions. These tables are also available on the
SOA and CAS Web sites. Since they will be included with the
examination, candidates will not be allowed to bring copies of the
tables into the examination room. A variety of tables will be provided to the
candidate in the study note package and at the examination. These
include values for the standard normal distribution, chi-square
distribution, and abridged inventories of discrete and continuous
probability distributions. These tables are also available on the
SOA and CAS Web sites. Since they will be included with the
examination, candidates will not be allowed to bring copies of the
tables into the examination room. Learning Outcomes The candidate is expected to be familiar with
survival, severity, frequency and aggregate models, and use
statistical methods to estimate parameters of such models given
sample data. The candidate is further expected to identify steps in
the modeling process, understand the underlying assumptions
implicit in each family of models, recognize which assumptions are
applicable in a given business application, and appropriately
adjust the models for impact of insurance coverage
modifications Learning Outcomes - Severity Models
- Calculate the basic distributional quantities:
- Moments
- Percentiles
- Generating functions.
- Describe how changes in parameters affect the
distribution.
- Recognize classes of distributions and their
relationships.
- Apply the following techniques for creating new families of
distributions:
- Multiplication by a constant
- Raising to a power
- Exponentiation
- Mixing
- Identify the applications in which each distribution is used
and reasons why.
- Apply the distribution to an application, given the
parameters.
- Calculate various measures of tail weight and interpret the
results to compare the tail weights.
- Explain the properties of the lognormal distribution.
- Explain the Black-Scholes formula as a limited expected value
for a lognormal distribution.
- Frequency Models
- For the Poisson, Mixed Poisson, Binomial, Negative Binomial,
Geometric distribution and mixtures thereof (as well as compound
distributions):
- Describe how changes in parameters affect the
distribution,
- Calculate moments,
- Identify the applications for which each distribution is used
and reasons why,
- Apply the distribution to an application given the
parameters.
- Aggregate Models
- Compute relevant parameters and statistics for collective risk
models.
- Evaluate compound models for aggregate claims.
- Compute aggregate claims distributions.
- For severity, frequency and aggregate
models
- Evaluate the impacts of coverage modifications:
- Deductibles
- Limits, and
- Coinsurance.
- Calculate Loss Elimination Ratios.
- Evaluate effects of inflation on losses.
- Risk Measures
- Calculate risk measures VaR, CTE and explain their use and
limitations
- Ruin Theory
- Calculate survival and ruin probabilities using discrete
models.
- Describe the considerations included in a ruin model
- Construction of Empirical Models
- Estimate failure time and loss distributions using
- Kaplan-Meier estimator, including approximations for large data
sets
- Nelson-Aalen estimator
- Kernel density estimators
- Estimate the variance of estimators and confidence intervals
for failure time and loss distributions.
- Estimate failure time and loss distributions with the Cox
proportional hazards model and other basic models with
covariates.
- Apply the following concepts in estimating failure time and
loss distribution
- Unbiasedness
- Consistency
- Mean squared error
- Construction and Selection of Parametric
Models
- Estimate the parameters of failure time and loss distributions
using
- Maximum likelihood
- Method of moments
- Percentile matching
- Bayesian procedures
- stimate the parameters of failure time and loss distributions
with censored and/or truncated data using maximum likelihood.
- Estimate the variance of estimators and the confidence
intervals for the parameters and functions of parameters of failure
time and loss distributions.
- Apply the following concepts in estimating failure time and
loss distributions
- Unbiasedness
- Unbiasedness
- Consistency
- Consistency
- Uniform minimum variance
- Determine the acceptability of a fitted model using
- Graphical procedures
- Kolmogorov-Smirnov test
- Anderson-Darling test
- Chi-square goodness-of-fit test
- Uniform minimum variance
- Credibility
- Apply limited fluctuation (classical) credibility including
criteria for both full and partial credibility.
- Perform Bayesian analysis using both discrete and continuous
models.
- Apply B�hlmann and B�hlmann-Straub models and understand the
relationship of these to the Bayesian model.
- Apply conjugate priors in Bayesian analysis and in particular
the Poisson-gamma model.
- Apply empirical Bayesian methods in the nonparametric and
semiparametric cases.
- Simulation
- Simulate both discrete and continuous random variables using
the inversion method.
- Estimate the number of simulations needed to obtain an estimate
with a given error and a given degree of confidence.
- Use simulation to determine the p-value for a hypothesis
test
- Use the bootstrap method to estimate the mean squared error of
an estimator.
- Apply simulation methods within the context of actuarial
models.
- Simulate lognormal stock prices
- Incorporate jumps in stock prices by mixing Poisson and
lognormal random variables.
- Use variance reduction techniques to accelerate
convergence.
- Use the Cholesky decomposition method for simulating correlated
random variables.
Text - Loss Models: From Data to Decisions, (Second Edition),
2004, by Klugman, S.A., Panjer, H.H. and Willmot, G.E., Chapter 3,
Chapter 4, Sections 4.1-4.6.6 only, Chapter 5, Chapter 6, Sections
6.1-6.7, 6.11.1 only, Chapter 7, Sections 7.1, 7.2.3, 7.3.1, 7.3.2
only, Chapters 9-11, Chapter 12 (excluding 12.5.4, 12.5.5 and
12.6), Chapter 13, and Chapter 17.
- # Derivatives Markets (Second Edition), 2006, by
McDonald, R.L., Chapters 18-19, excluding appendices.
Reading Options for Credibility
The candidate may use any of the alternatives shown below.
Option A - Loss Models: From Data to Decisions, (Second Edition), 2004, by
Klugman, S.A., Panjer, H.H., and Willmot, G.E., Chapter 16,
Sections 16.3, 16.4 (excluding16.4.7), 16.5 (excluding 16.5.3, 16.1
(background only), 16.2 (background only).
Option B - Foundations of Casualty Actuarial Science (Fourth Edition),
2001, Casualty Actuarial Society, Chapter 8, "Credibility", by
Mahler, H.C., and Dean C.G., Section 1 (background only) Sections
2-5 (Available as SN C-21-01).
- Topics in Credibility Theory (Study Note C-24-05) by Dean,
C.G.
Option C - Introduction to Credibility Theory (Third Edition), 1999,
Herzog, T.N., Chapter 1-3 (background only), 4-8, and 9 (background
only).
Specifically, the candidate is expected to be
able to perform the tasks listed below: Study Notes-Exam C (Construction and
Evaluation of Actuarial Models) Candidates should be sure to check this Study Note
Information page site periodically for additional corrections
or notices.
|
