Exam M   Actuarial Models

　　The examination for this material consists of five hours of multiple-choice questions offered in two independent segments: a 3-hour life contingencies segment (Exam MLC) and a 2-hour financial economics segment (Exam MFE).  Each segment will be graded separately.  In addition, a candidate will not be required to take both segments during the same exam administration period.
　　This material develops the candidate’s knowledge of the theoretical basis of certain actuarial models and the application of those models to insurance and other financial risks.  A thorough knowledge of calculus, probability and interest theory is assumed.  Knowledge of risk management at the level of Exam P is also assumed.
　　A variety of tables will be provided to the candidate in the study note package and at the examination.  These include values for the standard normal distribution and illustrative life tables.  These tables are also available on the SOA Web site.  Since they will be included with the examination, candidates will not be allowed to bring copies of the tables into the examination room.

　　LEARNING OUTCOMES ?C LIFE CONTINGENCIES SEGMENT

　　A. Survival and severity models.

　　1. Define 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. Calculate the expected values, variances, probabilities, and percentiles for survival-time random variables.
　　3. Define the continuous survival-time random variable that arises from the discrete survival-time random variable using a:
　　a) uniform distribution;
　　b) constant force of mortality; or
　　c) hyperbolic assumption.

　　B. Markov Chain Models

　　1. Define non-homogeneous and homogeneous discrete-time Markov Chain models and calculate the probabilities of
　　a) being in a particular state;
　　b) transitioning between particular states.

　　C. Life insurances and annuities

　　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.
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