Premium Calculation in Insurance

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F. Etienne De Vylder, Marc Goovaerts, J. Haezendonck
Springer Science & Business Media, Dec 6, 2012 - Mathematics - 564 pages
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I am pleased to participate in this Summer School and look forward to sharing some ideas with you over the next few days. At the outset I would like to describe the approach I will take in 1 presenting the material. I aim to present the material in a non rigorous way and hopefully in an intuitive manner. At the same time I will draw attention to some of the major technical problems. It is pitched at someone who is unfamiliar with the area. The results presented here are unfamiliar to actuaries and insurance mathematicians although they are well known in some other fields. During the next few minutes I will make some preliminary comments. The purpose of these comments is to place the lectures in perspective and motivate the upcoming material. After this I will outline briefly the topics to be covered during the rest of this lecture and in the lectures that will follow. One of the central themes of these lectures is RISK-SHARING. Risk-sharing is a common response to uncertainty. Such uncertainty can arise from natural phenomena or social causes. One particular form of risk-sharing is the insurance mechanism. I will be dealing with models which have a natural application in the insurance area but they have been applied in other areas as well. In fact some of the paradigms to be discussed have the capacity to provide a unified treatment of problems in diverse fields.
 

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Contents

Main lectures
19
Statedependent utility the demand for insurance
76
Separation of risk parameters
109
Practical models in credibility theory including
133
Rate making and the societys sense of fairness
151
The impact of reinsurance on the insurers risk
170
Net stop10ss ordering and related orderings
194
Limit theorems for risk processes
235
estimation of structural parameters
347
Population and social security projections for Bangladesh
363
Stability of premium principles under maximum entropy
381
Motor premium rating
398
The mean square error of a randomly discounted sequence
449
Simulation in actuaria1 work Some computational
466
The actuary in practice
489
Some BerryEsseen theorems for risk processes
505

estimation large sample theory
262
Rating of non proportional reinsurance treaties based
285
Resistant line fitting in actuarial science
315
Quantitative models of pension costs
333
Some notes on the methods of calculation of 1
518
A stochastic model for investment variables in
533
Index
561
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