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.

　　D. Poisson processes

　　1. Define Poisson process and compound Poisson process.
　　2. Define and calculate expected values, variances, and probabilities for Poisson processes,
　　a) using increments in the homogeneous case;
　　b) using interevent times in the homogeneous case;
　　c) using increments in the non-homogeneous case.

　　Note: Concepts, principles and techniques needed for Exam M are covered in the references listed below.  Candidates and professional educators may use other references, but candidates should be very familiar with the notation and terminology used in the listed references.

　　Texts - Life Contingencies Segment

　　• Introduction to Probability Models (Eighth Edition), 2003, by Ross, S.M., Chapter 5, Sections 5.3.1, 5.3.2 (through Definition 5.1), 5.3.3, 5.3.4 (through Example 5.14 but excluding Example 5.13), Proposition 5.3 and the preceding paragraph, Example 5.18, 5.4.1(up to example 5.23), 5.4.2 (excluding Example 5.25), 5.4.3, and Exercise 40.

　　And one of the following alternative references:

　　OPTION A
　　• Actuarial Mathematics (Second Edition), 1997, by Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J., Chapter 3, Chapter 4, Sections 4.1–-4.4, Chapter 5, Sections 5.1–5.4, Chapter 6, Sections 6.1(excluding utility-theory approach), 6.2–6.4, Chapter 7, Sections 7.1(excluding utility-theory approach), 7.2–7.6, Chapter 8, Sections 8.1–8.4, Chapter 9, Sections 9.1–9.5, 9.6.1, 9.7, 9.9, Chapter 10, Sections 10.1–10.4, 10.5–10.5.1, 10.5.4, 10.6, Chapter 11, Sections 11.1–11.3 and Chapter 15, Sections 15.1–15.2.1, 15.4, 15.6–15.6.1.

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]