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Introduction to
collective risk theory. Poisson processes. Loss distributions.
Distribution of aggregate claims. Ruin theory (Lundberg's
inequality). Heterogeneity models. Bayesian estimations. Buhlmann
and Buhlmann-Straub models. Application to group life insurance. The
individual risk model. Premium loading. Reinsurance. Excess of loss
reinsurance. Proportional reinsurance. Utility Functions. The
maximal expected utility criterion. Insurance applications. Premium
calculation principles: expected value, standard deviation,
variance, zero utility, exponential premium.
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Main textbooks: |
H. Bühlmann,
Mathematical Methods
in Risk
Theory,
Springer, 1996.
C. Daykin, T.
Pentikainen, M. Pesonen,
Practical Risk
Theory
for Actuaries,
Chapman & Hall, 1994. |
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Auxiliary
textbooks: |
H. Panjer, G.
Willmot,
Insurance Risk
Models,
Society of Actuaries, Schaumburg, IL, 1992.
S. Klugman, H.
Panjer, G. Willmot, G. Venter,
Loss Models:
From
Data
To
Decisions,
John
Wiley & Sons, 1998.
J.-P.Bouchaud, M.
Potters,
Theory of Financial
Risks.
From Statistical
Physics
to Risk
Management,
Cambridge University Press, 2001. |
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