Important external links
A MOOC: Intro to Actuarial Science
Link to the Sample SoA problems for FAM-S
Link to the Sample SoA solutions for FAM-S
Link to the Sample SoA problems for FAM-L
Link to the Sample SoA solutions for FAM-L
Our open-source textbook: Loss Data Analytics
Our open-source short course: Loss data short course
Lecture notes and the like
On R and RStudio
R will be used extensively in this course. Quizzes will
also (partially) be required to be completed in R. I
created some resources for Applied Statistics. They are linked
here:
Class 1: January 9th
Orientation.
First-Day Handout – 11am
First-Day Handout – 1pm
Modeling.
Slides: Actuarial Sims.
SIAM Videos on Mathematical Modeling
Quiz #1 – due on Wednesday, January 18th
Homework #1 – due on Friday, January 20th
Class 2: January 11th
Cumulative distribution
function. Survival function.
Class notes: Probability review: Random variables.
Lecture notes: The cumulative distribution function and friends
Problem Set #1 – problems
Problem Set #1 – solutions
Class 3: January 13th
Percentiles.
Value-at-Risk. (Sections 3.1.2,
4.1.1.3, 10.3.2)
Wikipedia: Value at Risk (VaR).
Discrete random variables. Probability mass function.
Lecture notes: Types of random variables.
Class notes: pmf.
Class 4: January 18th
Continuous random
variables. Probability density function. Mixed random variables.
Class notes: pdf. Mixed r.v.s
Quiz #1 – solutions
Quiz #2 – due on Wednesday, January 25th
Class 5: January 20th
The exponential
distribution.
Lecture notes: The exponential distribution.
Wikipedia: The exponential distribution.
Problem Set #2 – problems
Class notes: Independent r.v.s. The exponential distribution.
Problem Set #2 – solutions
Quiz #3 – due on Wednesday, February 1st
Quiz #4 – due on Wednesday, February 15th
Homework #1 – solutions
Homework #2 – due on Friday, January 27th
Class 6: January 23rd
Random number generation.
The inverse transform method (Section 6.1.2).
Wikipedia: Random number generation
Wikipedia: Mersenne twister
Lecture notes: The inverse transform method.
Lecture notes with proofs: The inverse transform method.
Class notes: The inverse transform method.
Quiz #5 – due on Wednesday, February 22nd
Basics of R.
Quiz #6 – due on Wednesday, March 1st
Quiz #7 – due on Wednesday, March 8th
Quiz #7 – this is
the Rmd file you can use to simply insert R-chunks with
your answers
Class 7: January 25th
R scripts and
R notebooks. For loops.
Functions in R. If ... else in
R. Simulations of random variables.
The R-script from class: For loops. Functions. If else.
The R-script from class: The exponential distribution.
Quiz #2 – solutions
Quiz #8 – due on Wednesday, March 22nd
Quiz #8 –
this is the Rmd file you can use to simply insert
R-chunks with your answers
Quiz #9 – due on Wednesday, March 29th
Quiz #9 –
this is the Rmd file you can use to simply insert
R-chunks with your answers
Class 8: January 27th
Focus on the expectation
(Section 3.1.1).
The tail formula for the expectation.
Class notes: The expected value.
Problem Set #3 – problems
Problem Set #3 – solutions
Homework #2 – solutions
Homework #3 – due on Friday, February 10th, 2023
Class 9: January 30th
TVaR (Section 10.3.3). Strong
Law of Large Numbers.
Class notes: The tail formula for the expectation. SLLN.
Class 10: February 1st
Asynchronous work due to winter
conditions.
Monte Carlo simulation. Basics of the binomial distribution.
Wikipedia: The Monte Carlo method.
Moments. Variance. Coefficient of variation (Section 3.1.1)
Class notes: Moments. Variance. Coefficient of variation.
Class 11: February 3rd
Asynchronous work due to winter
conditions.
Problem Set #4 – problems
Problem Set #4 – solutions
Class 12: February 6th
The excess loss random
variable. Per-payment and per-loss random variables (Section 3.4.1).
Class notes: Per payment and per loss random variables.
Suggested textbook examples: 3.4.1, 3.4.2
Homework #4 – due on Friday, February 17th, 2023
Class 13: February 8th
More on the per-payment
and per-loss random variables. The limited loss random variable.
Class notes: More on the per-payment and per-loss random variables. The limited loss random variable.
Quiz #3 – solutions
In-Term One: Topics
Practice for In-Term One – problems
Practice for In-Term One – solutions
Class 14: February 10th
Loss-modifications
demonstration.
Class notes: Even more on the per-payment and per-loss random variables. The limited loss random variable.
More Practice for In-Term One – problems
More Practice for In-Term One – solutions
Homework #3 – solutions
Class 15: February 13th
In-Term One
In-Term One – solutions
Class 16: February 15th
Franchise deductibles
(Sections
3.4.1).
Slides: Types of deductibles.
Loss elimination ratio (Section
3.4.1).
Other loss modifications (combined) (Section 3.4.2,
3.4.3).
Quiz #4 – solutions
Class 17: February 17th
Scale distributions.
(Section 3.3.2)
Slides: Scale distributions.
Homework #5 – due on Friday, February 24th, 2023
More on loss modifications (combined) (Section 3.4.2,
3.4.3).
Class notes: Parametric distributions. Scale distributions. Loss elimination ratio.
Suggested textbook examples: 3.4.3, 3.4.4, 3.4.5
Quiz #10 – due on Wednesday, April 5th
Homework #4 – solutions
Class 18: February 20th
Even more on loss
modifications.
Problem Set #5 – problems
Class notes: More policy modifications.
Problem Set #5 – solutions
Class 19: February 22nd
Proportional and excess
of loss reinsurance (Sections
3.4.4, 10.4).
Class notes: More on policy modifications. Reinsurance.
Homework #6 – due on Friday, March 3rd
mgf and pgf. Sums of independent random variables. (Sections 3.1.2, 3.1.3).
Central Limit Theorem.
Lecture notes: Generating functions.
Lecture notes: The Central Limit Theorem.
Suggested textbook examples: 3.1.1, 3.1.3, 3.1.4
Quiz #5 – solutions
Class 20: February 24th
The Poisson distribution
(Section
2.2.3.2).
Class notes: More on reinsurance. The Poisson distribution.
Homework #5 – solutions
Class 21: February 27th
Poisson distribution
practice.
Class notes: More on the Poisson distribution.
Class 22: March 1st
Poisson thinning. The
negative binomial distribution (Section
2.2.3.3).
Class notes: Poisson thinning. The negative binomial distribution.
Slides: The negative binomial distribution.
Quiz #11 – due on Wednesday, April 12th
Class 23: March 3rd
The binomial distribution
(Section 2.2.3.1).
The binomial-Poisson connection.
Class notes: The binomial distribution.
Suggested problem: Sample FAM-S Problem #25
Homework #6 – solutions
Quiz #12 – due on Wednesday, April 19th
Class 24: March 6th
The \((a, b, 0)\) class (Section 2.3). The \((a, b, 1)\) class (Section 2.5). On
compounding.
Class notes: \((a, b, 0)-\)class practice. On compounding.
Suggested textbook example: 5.5.2, 5.5.3
Homework #7 – due on Friday, March 10th
Class 25: March 8th
The impact of deductibles on
claim frequency (Section
5.5.2).
The individual risk model (Sections 5.2 and
5.3).
Class notes: The impact of deductibles on claim frequency. The individual risk model.
Monte Carlo for the individual risk model.
Quiz #7 – solutions
Class 26: March 10th
The collective risk
model.
Class notes: The collective risk model.
Homework #7 – solutions
In-Term Two: Topics
Practice for In-Term Two: problems
Practice for In-Term Two: solutions
Class 27: March 20th
Monte Carlo for the
collective risk model.
Stop-loss insurance (Section 5.3.2).
Class notes: The collective risk model [cont’d].
Homework #8 – due on Friday, March 24th
Class 28: March 22nd
Compound Poisson (Section 5.3.1: Special
case).
Class notes: Compound Poissons.
Quiz #8 – solutions
Class 29: March 24th
More on the stop-loss
insurance (Section
5.3.2). The interpolation theorem.
Problem: Stop loss.
Problem: The interpolation theorem.
Class notes: The net stop-loss premium. The interpolation theorem.
Homework #8 – solutions
Homework #9 – due on Friday, March 31st
(asynchronous content) The recursive formula for the
distribution of aggregate losses (Section 5.4.1).
Class notes: The recursive formula.
Class 30: March 27th
In-Term Two
In-Term Two: Solutions
Class 31: March 29th
Aggregate losses with an
ordinary deductible per-loss.
Slides: Effect of individual deductibles
Class notes: Deductibles and counts.
Quiz #9 – solutions
Homework #10 – due on Friday, April 7th
Class 32: March 31st
Maximum-likelihood
estimation: First principles. Individual unmodified data.
Slides: Maximum likelihood estimation.
Class notes: MLE
Homework #9 – solutions
Homework #11 – due on Friday, April 14th
Class 33: April 3rd
Maximum-likelihood
estimation: Grouped data.
Class notes: MLE (grouped data).
Class 34: April 5th
Maximum-likelihood
estimation: Truncation and censoring.
Class notes: MLE (censoring and truncation).
Quiz #10 – solutions
Class 35: April 7th
Maximum-likelihood
estimation: More on truncation.
Class notes: MLE (truncation practice).
Homework #10 – solutions
Class 36: April 10th
Maximum-likelihood
estimation: Bernoulli and Poisson.
Class notes: MLE (Bernoulli and Poisson).
Class 37: April 12th
Maximum-likelihood
estimation: Negative binomial.
Class notes: MLE (Negative binomial).
Quiz #11 – solutions
Class 38: April 14th
Maximum-likelihood
estimation: Binomial.
Hazard rate. Force of mortality. Survival analysis.
YouTube: The Gompertz-Makeham Law “Explained”
Maximum-likelihood estimation for mortality.
Wikipedia: Actuarial notation
Class notes: MLE (Binomial, mortality).
Homework #11 – solutions
In-Term Three: Topics
Practice for In-Term Three – problems
Practice for In-Term Three – solutions
Class 39: April 17th
Non-parametric
estimation.
Slides: Non-parametric. Nelson-Aalen
Class notes: MLE (Gompertz).
Class 40: April 19th
Nelson-Aalen.
Kaplan-Meier.
Slides: Kaplan-Meier
Class notes: Nelson-Aalen. Kaplan-Meier. More MLE.
Quiz #12 – solutions
Class 41: April 21st
Problem-solving
session.
Class notes: Problems.
Suggested problems: Sample FAM-S: Problems #2, #4, #23, #29, #37 (beware! their solution is wrong!), #42, #48, #49, #88, #89.
Class 42: April 24th
In-Term Three
In-Term Three – solutions
The Final Exam: Topics
Suggested problems: Sample FAM-L: Problems #2.3.
The Final Exam: Practice problems
The Final Exam: Practice solutions
