Schedule and Textbooks Information

Spring 2021 Schedule and Textbook Information for STAT 479

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STAT 479 - Textbook(s) for Spring 2021

CRN	Title	Author	ISBN	Version	Req/Opt
20399	Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance	Brown and Lennox	9781625424747	4th	N
20399	Loss Models: From Data To Decisions	Klugman, S., Panjer H., Willmot, G.	9781119523789	5th	N
29136	Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance	Brown and Lennox	9781625424747	4th	N
29136	Loss Models: From Data To Decisions	Klugman, S., Panjer H., Willmot, G.	9781119523789	5th	N
29432	Introduction to Ratemaking and Loss Reserving for Property and Casualty Insurance	Brown and Lennox	9781625424747	4th	N
29432	Loss Models: From Data To Decisions	Klugman, S., Panjer H., Willmot, G.	9781119523789	5th	N

STAT 479 - Schedule information for Spring 2021

CRN	Section	Instructor	Day	Time	Room
29136	OL1	Jianxi Su		0:0-0:0am	ASYNC ONLINE
20399	002	Jianxi Su	TR	4:30-5:45pm	SYNC ONLINE
20399	002	Jianxi Su	W	4:30-5:20pm	SYNC ONLINE
29432	003	Mengyi Xu	TR	3:00-4:15pm	SYNC ONLINE
29432	003	Mengyi Xu	W	3:30-4:20pm	SYNC ONLINE

STAT 479 - Course 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:

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:

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

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

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

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
a) Unbiasedness
b) Asymptotic unbiasedness
c) Consistency
d) Mean squared error
e) Uniform minimum variance
5. Determine the acceptability of a fitted model using
a) Graphical procedures
b) Kolmogorov-Smirnov test
c) Anderson-Darling test
d) Chi-square goodness-of-fit test
e) Likelihood ratio test