To consider some general models for mortality, to introduce life insurance policies, to introduce and develop the calculation of premiums, to introduce and develop the calculation of policy values.
1. Life insurance policies description and associated terminology (1.1 1. Life insurance terminology, e.g. premium, benefits, sum assured, policy term, 1.2 2. Description of life insurance policy types)
2. Numerical calculation of integrals (2.1 1. Trapezium rule, 2.2 2. Simpson's rule, 2.3 3. Evaluation of survival and mortality probabilties, and expected future lifetimes, from a deterministic force of mortality function.)
3. Survival models (3.1 1. Definition and properties of a future lifetime random variable, its distribution function and survival function, and is mean value and variance., 3.2 2. Concept of a limiting age, 3.3 3. Definition and properties of a force of mortality and its relationship with the distribution function, survival function and probability density function of the associated future lifetime random variable., 3.4 4. International actuarial notation for survival and mortality probabilities, and their relationship with the force of mortality, distribution function, survival function and probability density function of the corresponding future lifetime random variable., 3.5 5. International actuarial notation for the expected value of the future lifetime random variable, both the continuous and curtate forms., 3.6 6. Deterministic laws of mortality such as Gompertz's and Makeham's Laws.)
4. Single life insurance policy benefits - description and valuation (4.1 1. Mathematical and textual description of the contingent benefits paid from the following single-life contracts, calculation of the expected value and standard deviation, and related actuarial notation:, 4.2 a. Whole life insurance,, 4.3 b. Term insurance,, 4.4 c. Pure endowment,, 4.5 d. Endowment insurance,, 4.6 where contingent benefit payments are made at the end of the year of death, the end of a fraction of a year and immediately upon death, 4.7 2. Recursive relationships between the expected values of the above benefits., 4.8 3. Estimation of the expected value of insurance benefits when payments are immediately upon death and only the expected values when payments are made at the end of year of death are available, using , 4.9 a. the Claims Acceleration method,, 4.10 b. the Uniform Distribution of Deaths method., 4.11 4. Valuation of the simply vary insurance benefits.)
5. Life tables (5.1 1. Life table terminology e.g. radix, mathematical structure as expected values of random variables and actuarial notation e.g. l_x, d_x, 5.2 2. Fractional age assumptions: uniform distribution of deaths and constant force of mortality between integer ages., 5.3 3. Typical features of national mortality rates as age increases., 5.4 4. Underwriting and selection of lives from a population through underwriting, giving a different mortality for the selected lives versus the population., 5.5 5. Calculation of survival and mortality probabilities over the select period and beyond, into the ultimate life table,)
6. Single life annuity policy benefits - description and valuation (6.1 Mathematical and textual description of the contingent benefits paid from the following single-life contracts, calculation of the expected value and standard deviation, and related actuarial notation:, 6.2 a. Whole life annuities, paid in advance, in arrears and continuously,, 6.3 b. Temporary life annuities, paid in advance, in arrears and continuously,, 6.4 c. Deferred life annuities,, 6.5 d. Increasing whole life annuities,, 6.6 where contingent benefit payments are made continuously, and in advance and in arrears, at each year or fraction of a year., 6.7 2. Relationship between the expected values of the above benefits with each other and with those of life insurance contracts., 6.8 3. Estimation of the expected value of the life annuity contract when payments are continuously and at fractions of a year, when payments are made at each year are available, using different approximations e.g. Woolhouse's Approximation, Uniform Distribution of Deaths, 6.9 4. Valuation of the simply varying insurance benefits.)
7. Premiums for Life Insurance Policies (7.1 1. Equation of value for life insurance policies, 7.2 2. Net premium calculation using the principle of equivalence, 7.3 3. Gross premium calculation using the principle of equivalence, including different types of expenses, 7.4 4. With-profits policies also known as participating policies: associated terminology e.g. simple reversionary bonuses, compound reversionary bonuses, description and valuation.)
8. Policy Values (8.1 1. Motivation for and description of a policy value, 8.2 2. Definition and calculation of retrospective and prospective policy values, on both a net premium and gross premium basis., 8.3 3. Recursive formula for policy values)
By the end of the course, students should be able to do the following:
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SCQF Level: 10
Credits: 15