ACTUARIAL PRACTICE SOCIAL INSURANCE

1.Knowledge and understanding 

The  purpose  of  the  course  is  the  acquisition  of   theoretical principles concerning the life and non life insurance as well as pensions systems and social insurance. Beyond the indispensable theoretical knowledge, properly formalized, we also intend to transfer adequate professional skills to deepen the topics covered by an operational point of view.    
The teaching methodologies are designed to develop students’ professional skills using also multimedia, database access, use of spreadsheets, etc.  The  exam  is  composed  of  a  written  test  and  an  oral  examination,  withe  the  goal  of  testing  for  the  student’s knowledge, his understanding of the abstract concepts, and their translation  from an operational point of view.   During  the  entire  course,  knowledge  and  understanding  are  tested  on  a  continuous  basis,  and  a  fruitful  and active participation by students is always stimulated.   

2. Applying knowledge and understanding

Special attention is also paid to operating activities of future graduates, who are facing the problems professionally before mentioned, often under different assumptions or in different contexts, also transversal and interdisciplinary. To this end, teachers use a teaching method with the emphasis to the acquisition operations ("know-how") of the analytical tools and concepts proposed during the teaching of the discipline, aiming to develop critical skills of the student in a continuous process interaction analysis - synthesis, also presenting in the classroom appropriate real cases, guiding the study and analysis with the help of educational tools and technology more appropriate. Teachers care in its review of final learning the actual acquisition of these skills, even proposing and discussing critically and constructively with students drawn from them prepared with these precipue purposes.  

3. Making judgments  
The development of a critical ability in the context of the topics covered is a major educational objectives of teaching. A good acquisition of theoretical knowledge and operational chapabilities in the program of education is not enough for a complete training of the student if such preparation is not accompanied by the acquisition of a thorough, independent, socially and morally responsible for chapacity assessment, setting and resolution of a problem, proposing models that consider more appropriate analysis of financial issues considered. Such awareness serves as a guide to teachers throughout the training of discipline, making them interact with students in a constructive logic, in order to stimulate all phases of teaching, their chapacity for reflection, acquisition and interpretation of the information needed and Data essential, although insufficient or incomplete, for the management of complex issues, the construction and understanding of formal models, both descriptive and prescriptive. The focus is, therefore, training of research of economic and financial information sources, both traditional and modern, more appropriate (consultations of specialized publications, databases, websites, etc.),   

4. Communication skills

The   teaching  will  put  the  student  in  a  position  to transfer to third parties, even non-specialists, with clarity, precision and language appropriate technical, information, analysis, value judgments, projects and proposals on complex financial issues, that on the job  will face. The student is continually urged to make oral and formally their thoughts in proper arguments and techniques, to draft documents in writing, to prepare presentations multimedia, individually and in groups, to discuss what has been presented in the classroom, to stimulate a fruitful collaboration on the level of communication. The final exam is an additional chance for reflection and verification of the various communication skills actually achieved by the student. 5. Learning skills will provide students both an encouragement for a more active participation as possible to the entire educational process and for an improvement in the method of study and  the purpose of a more effective learning of the discipline, presenting characteristics precipue in terms of learning by means of an appropriate process inductive - deductive.    

  

The course starts by recalling basic concepts of probability theory. After the basic concepts of theory of insurance mainly related to the concepts of expected net present value and expected utility are introduced. After, the insurance portfolio management is discussed. Non life insurance and life insurance are presented. Finally, pension plans and health insurance are treated.

Probability theory. Probability and random events. Several types of porbability: classical probability; statistical probability and subjective probability. Total probability for incompatible events and composed probability for compatible events. Examples and appliations. Repeated trials. Random variables: basics, theorems and applications. Cumulative distribution functions of a discontinuous random variable. Bernoulli's Theorem. Probability of a given di deviation. De Moivre – Laplace's Theorem. Bienaymè Tchebycheff's Theorem. Probability distribution and its applications. 

Financial operations and insurance: operations under certainty and operations under uncertainty. Values, present values, expected values and expected net present values. The price in a financial operation under uncertainty. Expected value and variance. The utility function. The expected utiity criterion. Insurance applications.

The insurance portfolio management.Mutuality and solidarity in a portfolio. Uncertainty in the expenses of a portfolio. Risk and reinsurance. Technical and practical aspects of reinsurance. Insurance portfolio management: time dimension. .

Non-life insurance. 

Life tables. Life insurance. Mathematical reserve.

Finance in life insurance: linking benefits to the investment performance. Adjusting benefits.  Participating policies. Unit-linked policies. Index-linked policies. Universal Life policies.

Life insurance pricing. Single premiums. Periodic premiums. Loading for expenses. Premium components.Expenses and loading for expenses. The expense-loaded premiums. 

Pension plans. Health insurances. 

Overview of multi-criteria decision analysis: Methods based on a multi-attribute value function; Outranking methods (ELECTRE and PROMETHEE methods); Decision rule-based methods; Interactive multi-objective optimisation methods. Analytical Hierarchy Process; Best and Worst method; Deck of Cards method. Ordinal regression; Robust ordinal regression; Stochastic ordinal regression.

Ermanno Pitacco, Elementi di Matematica delle assicurazioni, Lint, Trieste 2009. 

Olivieri, Annamaria, and Ermanno Pitacco. Introduction to Insurance Mathematics: Technical and financial features of risk transfers. Springer, 2015.

Supporting materials will be provided for the part on probability theory and the part on multicriteria decision analysis.

1. What is the difference between classical, statistical and subjective probability?

2. Can you tell me about total probabilities for incompatible events?

3. Can you tell me about compound probabilities for sampled events? 

4. What is a distribution function?

5. Can you tell me Bernoulli's theorem? Can you tell me Bienaymè Tchebycheff's theorem?

6. What is a certain financial transaction? What is a random financial transaction?

7. What is present value? What is expected value? What is expected present value?

8. Tell me about expected utility and its application in insurance?

9. What is the difference between mutuality and solidarity in a portfolio? 

10. Can you tell me what reinsurance is and explain its technical and practical aspects?

11. Can you tell me about the insurance premium in non-life insurance?

12. What is the difference between fair premium and pure premium?

13. What is a bonus malus tarrifation system?

14. Tell me about premium and technical reserve management in non-life insurance

15. Tell me about the demographic basis of life insurance?

16. What are survival tables? What are projected tables?

17. Tell me about life insurance?

18. Tell me about insurance in case of death?

19. Can you tell me about mixed insurance?

20. What are single premium and periodic premiums? How are they calculated?

21. What is a natural prize?

22. What is the mathematical reserve? What are pure mathematical reserve, prospective reserve and retrospective reserve? 

23. What are index-linked insurance and revaluable insurance?

24. What are unit-linked insurance, index-linked insurance and universal life insurance?

25. What is the premium rate? 

26. Tell me about the implementation of supplementary pensions?

27. Tell me about health insurance?

28. What is a multi-attribute aggregation function?

29. What is the Choquet integral?

30. Tell me about ELECTRE methods?

31. Can you tell me about PROMETHEE methods?

32. Tell me about the Dominance-based Rough Set Approach?

33. What is interactive multi-objective optimisation?

34. Tell me about the Analytical Herarchy Process?

35. Tell me about the Best and Worst method?

36. Tell me about the pack of cards method?

37. What is ordinal regression?

38. What is robust ordinal regression?

39. What is stochastic regression?