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After following this course the student:
- has insights in human mortality models and human mortality data;
- has knowledge of a general framework for the valuation of life contingent liabilities where cash flows depend on the future lifetime of one insured or multiple insureds;
- is able to calculate actuarial present values, premium structures and policy values for different types of life annuity and life insurance products;
- is able to do this type of calculations in both discrete and continuous time for one and multiple insureds;
- is able to understand and to use the relevant international actuarial notation for life contingent risks.
The course covers the following topics:
- a general introduction to life contingent risks and related financial products
- a discrete time framework to value cash flows over time with a discussion of: discount functions, interest and discount rates, actuarial equivalence of cash flow vectors, balances and reserves for a given cash flow vector and prospective and retrospective views
- the life table, human mortality data and their characteristics, demographic markers, calculating probabilities using the data published in a life table and choice of life tables
- life annuity products, calculating actuarial present values and premiums
- life insurance products, calculating actuarial present values and premiums
- policy values for annuity and life insurance products, a general framework, recursions, and detailed insights
- working with fractional durations
- working in continuous time and extending all topics studied before from discrete to continuous setting
- select mortality
- multiple-life contracts, the joint life status, the last survivor status, annuities and insurances on multiple lives
- multiple decrement theory
- expenses and profits.
The course recommends a basic understanding (at the level of the first year of a BSc in a quantitative study program) of algebra, analysis and probability theory.
The course is organized as follows: every week
- two lectures of two hours;
- a tutorial session of two hours covering exercises;
- a computer session of two hours with assignments that have to be solved with R.
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