Probability Models with Actuarial Applications (M339J)

    Important external links
  • The STAM Exam curriculum
  • The STAM Exam tables
  • Link to the Sample SoA problems for STAM
  • Link to the Sample SoA solutions for STAM


    • Class 1: January 22nd
    Orientation.
  • First-Day Handout


    • Class 2: January 24th
    Modeling.
  • Actuarial Sims.
    • Random variables.
  • On random variables.
  • Class notes: Severity. Frequency. The indicator random variable.


    • Class 3: January 27th
    Probability mass function. Probability density function.
  • Class notes: pmf.pdf.
  • Homework #1 -- due on Monday, February 3rd


    • Class 4: January 29th
    Moments.
  • Moments.
  • Quiz #1 -- due on Wednesday, February 5th


    • Class 5: January 31st
    Focus on the expected value.


    Class 6: February 3rd
    More moments. Modifications.
  • Homework #1 -- Solutions


    • Class 7: February 5th
    The per-loss and per-payment random variables.
  • Class notes: The per-loss and per-payment random variables.
  • Quiz #1 -- Solutions
  • Homework #2 -- due on Thursday, February 13th


    • Class 8: February 7th
    Percentiles. Central Limit Theorem. mgf and pgf.
  • Percentiles. Central Limit Theorem. mgf and pgf. Heavy tails.
  • Class notes: Percentiles. pgf.


    • Class 9: February 10th
    Heavy tails. Risk measures. Parametric distributions.
  • Parametric distributions.
  • Class notes: Sums of independent random variables. Scaling.


    • Class 10: February 12th
    More on scale distributions and k-point mixtures.
  • Class notes: Scale distributions. k-point mixtures.
  • Homework #2 -- Solutions


    • Class 11: February 14th
    Continuous models.
  • Continuous models.
  • Class notes: k-point mixtures. Transformations.
  • In-Term One -- practice problems
  • Practice for In-Term One -- Solutions
  • Quiz #2 -- due on Tuesday, February 18th
  • Quiz #3 -- due on Thursday, February 20th


    • Class 12: February 17th
    More on transformations. Mixing distributions.
  • Class notes: Powers of random variables. Mixing.
  • Homework #3 -- due on Monday, February 24th


    • Class 13: February 19th
    More on mixing distributions.
  • Class notes: Mixing. Splicing.
  • Quiz #2 -- Solutions


    • Class 14: February 21st
  • In-term exam I
  • In-Term One -- Solutions
  • Quiz #3 -- Solutions


    • Class 15: February 24th
    Per loss and per payment r.v.s [revisited].
  • Per loss and per payment.
  • Class notes: Ordinary deductible [revisited]. Franchise deductible.
  • Homework #3 -- Solutions
  • Homework #4 -- due on Monday, March 2nd


    • Class 16: February 26th
    The loss elimination ratio.


    Class 17: February 28th
    Further policy modifications.


    Class 18: March 2nd
    The Poisson distribution.
  • Class notes: Policy modifications. The Poisson distribution.
  • Homework #4 -- Solutions


    • Class 19: March 4th
    The negative binomial distribution.
  • The negative binomial distribution.


    • Class 20: March 6th
    The Poisson-gamma mixture. The binomial distribution.


    Class 21: March 9th
    The (a, b, 0) class. Modified and truncated distributions.


    Class 22: March 11th
    The effect of deductibles on claim frequency.


    Class 23: March 13th
    No classes at UT.
  • The updated First-Day Handout
  • Quiz #4 -- due on Wednesday, April 1st
  • Homework #5 -- due on Friday, April 3rd


    • Class 24: March 30th
    Getting used to ZOOM.
  • In-Term Two -- Topics
  • Practice for In-Term Two -- Problems
  • Practice for In-Term Two -- Solutions


    • Class 25: April 1st
    Problem-solving session: Mixing distributions and discrete distributions.
  • Quiz #4 -- Solutions


    • Class 26: April 3rd
    Problem-solving session: Policy modifications.
  • Homework #5 -- Solutions
  • Mock In-Term Two -- Problems
  • Mock In-Term Two -- Solutions


    • Class 27: April 6th
  • In-term exam II
  • In-Term Two


    • Class 28: April 8th
    Aggregate loss models.

    Class 29: April 10th
    Stop-loss insurance. Interpolation theorem.


    Class 30: April 13th
    Compound Poissons.


    Class 31: April 15th
    The recursive formula for the distribution of aggregate losses.


    Class 32: April 17th
    Aggregate payments.
  • Aggregate claims.


    • Class 33: April 20th
    More on aggregate payments.


    Class 34: April 22nd
    Maximum-likelihood estimation: First principles. Individual unmodified data.


    Class 35: April 24th
    Maximum-likelihood estimation: Grouped data.
  • Quiz #5 -- due on Monday, April 27th
  • Homework #6 -- due on Friday, May 1st
  • Homework #7 -- NOT TO BE HANDED IN
  • Homework #7 -- Solutions


    • Class 36: April 27th
    Maximum-likelihood estimation: Truncation and censoring.
  • Quiz #5 -- Solutions


    • Class 37: April 29th
    Maximum-likelihood estimation: Bernoulli and Poisson.
  • In-Term Three -- Topics
  • Practice for In-Term Three -- Problems
  • Practice for In-Term Three -- Solutions
  • Quiz #6 -- due on Monday, May 4th


    • Class 38: May 1st
    Maximum-likelihood estimation: Negative binomial and binomial.
  • Homework #6 -- Solutions
  • Homework #8 -- due on Friday, May 8th


    • Class 39: May 4th
    Variance and interval estimation.
  • Quiz #6 -- Solutions
  • Mock In-Term Three -- Problems
  • Mock In-Term Three -- Solutions


    • Class 40: May 6th
  • In-term exam III
  • In-term Exam #3 -- Solutions


    • Class 41: May 8th
    The delta method.
  • Homework #8 -- Solutions