Stat 479: Loss Models (Banner Course Number: 47900)

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Fall 2009 textbook is:

Klugman, Panjer and Willmot, Loss Models: From Data to Decision, 3rd Edition, Required



Outline:

Specifically, the candidate is expected to be able to perform the tasks listed below:

A. Severity Models
  1. Calculate the basic distributional quantities:
    a) Moments,
    b) Percentiles,
    c) Generating functions.
  2. Describe how changes in parameters affect the distribution.
  3. Recognize classes of distributions and their relationships.
  4. Apply the following techniques for creating new families of distributions:
    5. a) Multiplication by a constant,
    b) Raising to a power,
    c) Exponentiation,
    d) Mixing.
  5. Identify the applications in which each distribution is used and reasons why.
  6. Apply the distribution to an application, given the parameters.
  7. Calculate various measures of tail weight and interpret the results to compare the tail weights.
  8. Explain the properties of the lognormal distribution.
B. Frequency Models
a. 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.
C. Aggregate Models
  1. Compute relevant parameters and statistics for collective risk models.
  2. Evaluate compound models for aggregate claims.
  3. Compute aggregate claims distributions.
D. For severity, frequency and aggregate models,
  1. Evaluate the impacts of coverage modifications:
    2. a) Deductibles,
    b) Limits, and
    c) Coinsurance.
  2. Calculate Loss Elimination Ratios.
  3. Evaluate effects of inflation on losses.
E. Risk Measures
  1. Calculate risk measures VaR, CTE and explain their use and limitations
F. Ruin Theory
  1. Calculate survival and ruin probabilities using discrete models.
  2. Describe the considerations included in a ruin model
G. Construction of Empirical Models
  1. Estimate failure time and loss distributions using
    2. a) Kaplan-Meier estimator, including approximations for large data sets
    b) Nelson-Aalen estimator
    c) Kernel density estimators
  2. Estimate the variance of estimators and confidence intervals for failure time and loss distributions.
  3. Estimate failure time and loss distributions with the Cox proportional hazards model and other basic models with covariates.
  4. Apply the following concepts in estimating failure time and loss distribution
    5. a) Unbiasedness
    b) Consistency
    c) Mean squared error
H. Construction and Selection of Parametric Models
  1. 1. Estimate the parameters of failure time and loss distributions using
    2. a) Maximum likelihood
    b) Method of moments
    c) Percentile matching
    d) Bayesian procedures
  2. Estimate the parameters of failure time and loss distributions with censored and/or truncated data using maximum likelihood.
  3. Estimate the variance of estimators and the confidence intervals for the parameters and functions of parameters of failure time and loss distributions.
  4. Apply the following concepts in estimating failure time and loss distributions
    5. a) Unbiasedness
    b) Asymptotic unbiasedness
    c) Consistency
    d) Mean squared error
    e) Uniform minimum variance
  5. Determine the acceptability of a fitted model using
    6. a) Graphical procedures
    b) Kolmogorov-Smirnov test
    c) Anderson-Darling test
    d) Chi-square goodness-of-fit test
    e) Likelihood ratio test