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## Syllabus

EN IT

### Learning Objectives

LEARNING OUTCOMES:
The objective of this course is to understand the main mathematical techniques for the modelling and the analysis of insurance markets.

KNOWLEDGE AND UNDERSTANDING:
The course discusses the main determinisic and stochastic methord for modelling the insurance market and pricing life insurance policies.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Students will be able to describe in mathematical terms, the main models which are commonly used in managing and pricing of life insurance contracts, and to indentify their main characteristics. Students will also be able to apply quatitative techniques for evaluating different types of insurance policies.

MAKING JUDGEMENTS:
The course contains proofs of theorems and analytic properties. These aspects allows students to build and develop logic arguments with a clear identification of hypotheses and theses, and identify wrong or incorrect reasoning. The discussion of examples and model in actuarial science will permit the students to understand the main characteristics of a reasonable mathematical modelling of some phenomena.

COMMUNICATION SKILLS:
Students must be able to describe with the due scientific rigour, mathematical models for representing longevity risk and discuss the necessary techniques for the valutaion of life insurance contracts. This course provides all the instruments for communicating rigorously quantitative results in the actuatial framework.

LEARNING SKILLS:
The course provides basic instruments for the development of further studies in the actuarial framework. The more theoretical part allows students to independently face new and more complex problems.

### Prerequisites

Probability (Discrete and continuous random variables, expectations, conditional probability)

### Program

1.Reminder on Compound Interest
2.Survival probability
3.Life Insurance contracts
4.Life Annuities
6.Multiple Life Insurance

### Books

1. Life insurance mathematics. Hans U. Gerber. With exercises contributed by Samuel H. Cox. 3rd ed. Springer, 1997.

2. Actuarial Mathematics for Life Contingent Risks. David C. M. Dickson, Mary R. Hardy, Howard R. Waters. 3rd ed. Cambridge University Press, 2020.

### Bibliography

1. Life insurance mathematics. Hans U. Gerber. With exercises contributed by Samuel H. Cox. 3rd ed. Springer, 1997.

2. Actuarial Mathematics for Life Contingent Risks. David C. M. Dickson, Mary R. Hardy, Howard R. Waters. 3rd ed. Cambridge University Press, 2020.

### Teaching methods

Theoretical lectures and exercises

### Exam Rules

Attending students (at most 3 missing lectures).

To verify learning you will be given home assignments and there will be a final oral examination to be done at the first exam call (December). In assignments and the oral exam you will be asked to solve exercises and to answer theoretical questions on topics covered during letures.

Non-attending students and attending students who do not deliver assignements in due time.

Learning will be verified through a written exam where you will be asked to solve exercises and to answer theoretical questions on topics covered during letures.

Students must demonstrate to be able to determine survival probability of an individual using the models studied in classes and mortality tables and to know their properties; to be able to distinguish life insurance contracts, both classical and modern, and to comment on their characteristics; to be able to determine, both theoretically and with the help of electronic paper sheet, the actuarial value of these contracts, the loss process, premiums, and other important quantities such as net amount at risk, risk premium and saving premium.