教學大綱 Syllabus

課程簡介Course Description

The course is designed to provide postgraduate students the fundamentals of actuarial mathematics as follows.
1. Define present-value-of-benefit random variables defined on survival-time random variables:
a) for one life, both in the single- and multiple-decrement models;
b) for two lives, where the lives are independent or dependent (including the common shock model).

2. Define and calculate the expected values, variances and probabilities for:
a) present-value-of-benefit random variables;
b) present-value-of-loss-at-issue random variables, as a function of the considerations
(premiums);and
c) present-value-of-loss random variables, as a function of the considerations (premiums).

3. Calculate considerations (premiums) for life insurances and annuities,
a) using the Equivalence Principle; and
b) using percentiles.

4. Calculate liabilities, analyzing the present-value-of-future-loss random variables:
a) using the prospective method;
b) using the retrospective method;
c) using special formulas.

5. Calculate
a) gross considerations (expense-loaded premiums);
b) expense-loaded liabilities (reserves);
c) asset shares.

6. Using recursion, calculate expected values (reserves) and variances of present-value-of-future loss random variables for general fully-discrete life insurances written on a single life.

7. Extend the present-value-of-benefit, present-value-of-loss-at-issue, present-value-of-future loss random variables and liabilities to discrete-time Markov Chain models, to calculate
a) actuarial present values of cash flows at transitions between states;
b) actuarial present values of cash flows while in a state;
c) considerations (premiums) using the Equivalence Principle;
d) liabilities (reserves) using the prospective method.