This course explain the models used to project cash flows for basic traditional and non-traditional life insurances; calculate policy values and present values of the cash flows for basic traditional and non-traditional life insurances; explain and calculate the benefit reserve for basic traditional and non-traditional life insurances; explain the relationship between expenses and gross premium and calculate contract level values based on the gross premium for life insurances and annuities; understand the multiple decrement theory and applications, multiple state models, multiple life functions, and the interest risk.
Tutorial 1: Policy Values I - Present Value of Future Loss Random Variable; Premium Reserve (or Benefit Reserve) by Prospective Formula; Variance of Present Value of Future Loss Random Variable; Premium Reserve by Retrospective Formula.
Tutorial 2: Policy Values II - Thiele's Differential Equation for Premium Reserve; Numerical Solution of Thiele's Differential Equation; Recursive Formula for Premium Reserve.
Tutorial 3: Policy Values III - Expense Reserve; Annual Profit and Gain by Source; Asset Shares.
Tutorial 4: Multiple Decrement Models I - Multiple Decrement Probabilities; Multiple Decrement Life Table; Forces of Decrement.
Tutorial 5: Multiple Decrement Models II - Associated Single Decrement Model; Fractional Age: Constant Force of Decrement; Fractional Age: Uniform Distribution of Decrement (UDD) in Multiple Decrement Table; Fractional Age: Uniform Distribution of Decrement (UDD) in Associated Single Decrement Tables.
Tutorial 6: Multiple Decrement Models III - Discrete Decrements; Expected Present Value, Premium, and Policy Value.
Tutorial 7: Multiple State Models I - Multiple State Models; Discrete Time Markov Chains; Continuous Time Markov Chains: Direct Calculation.
Tutorial 8: Multiple State Models II - Continuous Time Markov Chains: Kolmogorov's Forward Equations; Expected Present Value and Premium; Policy Value and Thiele's Differential Equation.
Tutorial 9: Multiple Lives Models I - Multiple Lives Models; Probability Framework for Multiple Lives Models; Joint Life Status and Probabilities; Last Survivor Status and Probabilities.
Tutorial 10: Multiple Lives Models II - Important Relationship between Joint Life and Last Survivor Statuses; Expectation, Variance, and Covariance of Future Lifetimes; Insurances and Annuities for Joint Life and Last Survivor Statuses.
Tutorial 11: Multiple Lives Models III - Contingent Probabilities; Contingent Insurances.
Tutorial 12: Multiple Lives Models IV - Reversionary Annuities; Common Shock Model.
1. Dickson, C. M. D., Hardy, M. R., and Waters, H. R. (2013). Actuarial Mathematics for Life Contingent Risks, 2nd edition, Cambridge University Press.
2. Bowers, N. L., Gerber, H.U., Hickman, J.C., Jones, D.A., and Nesbitt, C.J., 1997. Actuarial Mathematics, 2nd edition, Schaumburg, Ill.: Society of Actuaries.