Stat-575. Actuarial Modeling.

HOMEWORK HANDOUTS

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Instructor: Professor Vladimir Rotar; Office GMCS-514, phone: 594 7244; e-mail: rotar@sciences.sdsu.edu or vrotar@euclid.ucsd.edu.

Texts:

1. Actuarial Models: The Mathematics of Insurance, by V.I.Rotar, 2006.

2. Actuarial Mathematics, by N.L Bowers et al., 2000.

In this course we will examine various models of insurance processes and key aspects of the insurance market, including

the evaluation of risk, types of insurance, distributions of possible damages (in the case of casualty insurance) and human lifetimes (in the case of life insurance), principles used by insurance companies in managing their activities.

SYLLABUS (with sections of the book [1]) .

The list below is one of topics, not of lectures. A real experience may dictate a slower or faster pace. A slight change of the order of exposition and even of the contents is also possible.

1. Introduction. Comparison of random variables. Optimal insurance. (Ch.1: 1.1, 1.2.1-2, 2.1, 3.1-2, 5.1)
2. Individual risk models for a short term. (Ch.2: 1.1.1-3, 1.2-3)
3. Collective risk models for a single period. Compound Poisson distribution. (Ch.4: 1, 2.1, 3.1-2, 4.1-2)
4. Collective risk models over an extended period. Insurance processes in time. The flow of claims, compound Poisson process, some more general schemes. (Ch.5: 1.1, 1.2.1, 2.1, 3)
5. Ruin probability. (Ch.7: 1.2.1-2, 2.4)
6. Survival distributions and Life Tables. (Ch.8: 1.1-6)
7. Types of life insurance. Actuarial present values (APV). (Ch.9: 1, 2.1.1-2, 2.2-4)
8. Life annuities, APV for different types of annuities.(Ch.10: 1,2, 3.1-3)
9. Different principles of the determination of premiums. Percentile and benefit premiums for different type of insurance. (Ch11: 2.1, 2.2.1-2, 2.4.2)
10. Benefit reserves. (Some material from Ch.11: 3)