Week |
Subject |
Related Preparation |
1) |
Review of probability. Discrete and continuous random variables and their distributions. |
|
2) |
Measures of location and dispersion. Expectation and moments.
Moment generating functions. |
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3) |
Loss Distributions. |
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4) |
Conditional distributions, conditional expected value and variance. Methods of creating new distributions. Prior and posterior distributions. |
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5) |
Point estimation and method of moments. Maximum likelihood and confidence intervals. Fitting loss distributions. |
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6) |
Aggregate loss models, the compound model for aggregate claims.Computing the aggregate loss distribution. |
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7) |
The individual and collective risk models. |
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8) |
Distribution of the aggregate claim amount. Compound Poisson models, recursive formula, approximations.Introduction to ruin problems. |
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9) |
Ruin probability in the short term, factors effecting probability of ruin.Effect of reinsurance. |
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10) |
Continuous time ruin models. The Poisson process, Lundberg's inequality and the adjustment coefficient. |
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11) |
Introduction to credibiity theory. Classical credibility, full and partial credibility. Aims of credibility models. |
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12) |
Credibility theory continued. Bayesian credibility. Bühlmann and Bühlmann and Straub models. |
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13) |
Experience rating and bonus malus systems. |
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14) |
Review and applications. |
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15) |
Final exam. |
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16) |
Final exam. |
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Course Notes / Textbooks: |
Hossack, I., Pollard, J,H., Zehnwirth, B., ‘Introductory statistics with applications in general insurance’.
Klugman, S., Panjer, H., Willmot, G., (2004) Loss Models, From Data to Decisions,John Wiley and Sons.
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References: |
Daykin, C, Pentikainen, T., Pesonen, M.(1994) Practical Risk Theory for Actuaries, Chapmann and Hall.
Werner, G., Modlin, C, Basic Ratemaking, CAS study notes. |
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Program Outcomes |
Level of Contribution |
1) |
Ability to assimilate mathematic related concepts and associate these concepts with each other.
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2) |
Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
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2 |
3) |
Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. |
2 |
4) |
Ability to make individual and team work on issues related to working and social life. |
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5) |
Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
2 |
6) |
Ability to use mathematical knowledge in technology. |
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7) |
To apply mathematical principles to real world problems. |
2 |
8) |
Ability to use the approaches and knowledge of other disciplines in Mathematics. |
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9) |
Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
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10) |
To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. |
3 |
11) |
To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. |
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12) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, |
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