Section 0101, MWF 2, Rm 0407
Spring 2006
Click here
for solutions to final exam.
See below for:
Take-Home
Exam Problems due 5/17/06
NOTE: do the most current versions of
the Exam problems: a few of them
have been corrected to be clearer and
easier than the ones handed out in class.
Getting Started in R.
Homeworks.
Sample Problems for In-Class Test.
Instructor: Eric Slud, Statistics Program & Actuarial Advisor
Objective: This course introduces
several of the major mathematical ideas
involved in calculating
life-insurance premiums, including: compound interest and
present valuation of future income streams; probability
distributions and expected
values derived from life tables; the
interpolation of probability distributions from values
estimated
at one-year multiples; the `Law of Large Numbers' describing the regular
probabilistic behavior of large populations of independent
individuals; and the detailed
calculation of expected present
values arising in Insurance problems.
Prerequisite: Calculus through Math
240-241. Some Probability at the level of
Stat 400 would be helpful. Ideas from probability and statistics will
be developed as
needed, through course notes and reference to the Stat 400 text,
Introduction
to Probability
and Statistics, 6th ed. (2004) by R. Devore. However,
this material may go a little quickly
if you have really never been exposed to it before.
Main Text: Book notes (written by
me) available here
for download, one chapter at a time.
(It is currently in a single pdf-file. Individual chapters will
be revised and placed in the
same directory, with revision dates,
as the term goes on.)
Recommended Texts:
(1) Life Insurance Mathematics 3rd ed. (1997), by
H. Gerber, with
Exercises by S.H. Cox, Springer-Verlag.
(2) Theory of Interest and Life Contingencies With Pension
Applications: A Problem
Solving Approach, 3rd ed. (1999) by Michael M. Parmenter,
ACTEX Publications.
I will probably place these on reserve in EPSL.
Course format: Graded homeworks
(one every 1.5 weeks) , one in-class midterm just
before
Spring Break in March, and a final exam which may take the form of
a take-home final or
project. Homework counts 40%, and midterm and
final/project each count 30%, toward the
course grade.
Project and/or take-home topics will be distributed and discussed
after the mid-term.
Homeworks:
will regularly be posted
here
. Any changes (such as changes in due-date,
corrections of misprints, etc.) and hints will also be
posted to the same "HWx.txt" page
where the homework is assigned.
To see a sample of problems
for the In-Class Test on Friday 3/31/06, click here.
This Sample was the Test I gave in Spring 2001. The Test Friday
will not
necessarily follow exactly the same format or
problem types, but the level
of difficulty will be about the
same.
For solutions to the Sample Test, click here .
Project/Final: in lieu of an
in-class final exam, I have sometimes given
either a 10-12
problem take-home consisting
of problems on the
course material from
past actuarial exams, OR of doing a 5-10 page
Project paper on some additional topic related
to the course material.
Guidelines for Projects can be found here.
Take-Home Problems for Final
would be handed out in class a little less than
2 weeks
before the Final Exam date, and would be due at the scheduled time of
the
Final Exam. I will make up a new set of problems to reflect the
level of old and
recent "Course 150" Actuarial exams.
Click
here for Take-Home. (But make sure to do the most current version.)
HANDOUTS & EXHIBITS
(1) An R program Balance.Discrete
to calculate accumulated balances from streams of
deposits (or
withdrawals, treated as negative deposits) over a series of times,
with possibly
time-varying but piecewise interest rates which
can change just after each deposit.
(2) A MATLAB program RefExmp.m
to calculate quantities related to mortgage
refinancing. Once you understand what it calculates, you may (and probably
should, unless
you prefer another programming platform like a spreadsheet) use it
in Homework Set 3.
COURSE OUTLINE
I. Overview of actuarial mathematical problems.
A. Theory of interest
and actuarial notation.
II. Introduction to Life Tables & Mortality Measurements.
A. Probability
densities, random variables, expectation, law of large numbers.
B. Relative
frequencies and empirical death rates. Connections with
probabilities.
C. Survival curves.
Force of mortality (hazard rates).
D. Theoretical
survival models. Estimation from life-table data.
i. Stochastic simulation of insurance experience.
E. Actuarial approximations for survival probabilities.
F. Probability
in demography: stationary populations and age-distributions.
III. Calculation of Insurance Premiums. Valuation of insurance contracts. Reserves.
For the systematic Introduction to R and R reference manual
distributed with the R software,
and for software you can
download free, visit the R website .