ADVANCED INSURANCE AND ACTUARIAL METHODS

The course belongs to the two curricula “Economics-QEM” and “Finance”, and will allow the students to acquire a solid theoretical and quantitative grounding about insurance and actuarial methods. The main objectives of the course are
• to acquire knowledge about the different insurance products;
• to provide the students with the necessary theoretic knowledge about the concepts of risk and risk-pooling, and the role of an insurance company;
• to understand the main aspects of life insurance, with respect to mortality trends, risk margins, profit assessment, and linking life insurance benefits to the investment performance;
• to understand the foundations of post-retirement income and contribution pension plans.

1. Knowledge and understanding:
• To understand the different definitions of “risk” and the fundamental features of life insurance, together with the basic contract structures;
• To understand the main life insurance products;
• To understand the main non-life insurance products;
• To understand the functioning of insurance companies and the markets of insurance products;
• To understand the basic quantitative models for the evaluation of the main insurance products;
• To understand the riskiness of a portfolio of risks and the transfer of risks.

2. Ability to apply knowledge and understanding:
• To be able to compute the net premium and the fair value of life insurance contracts;
• To be able to apply the bonus-malus system;
• To be able to quantify the technical reserves;
• To be able to use the survival distribution functions and life tables;
• To be able to communicate to others the knowledge acquired.

3. Ability to make judgements:
• Ability to choose the most suitable insurance products to cover specific insurable risks;
• Ability to determine if the market premium for a life insurance product is correctly determined.

4. Ability to communicate
• To be able to communicate to others the knowledge acquired;
• To be able to interact with his/her peers and tutor.

5. Ability to learn
• To be able to take notes and to share them on-line;
• To be able to look into the textbooks and the bibliography therein.

Students are expected to know the basic elements of financial mathematics, as they are taught in a course of Financial Mathematics at the laurea/bachelor degree:
• Basics of interest rates;
• Annuities;
• Amortization of a debt.

Students are also expected to be familiar with the following elements of calculus:
• Single variable functions;
• Several variable functions.
• Derivatives;
• Integrals.

Risks and insurance
• Definition of risk;
• Risks inherent in the individual lifetime;
• Managing risks;
• Risk identification and risk assessment;
• Models for risk assessment;
• Risk measures;
• Transferring risks and building up a pool;
• The role of the insurer.

Managing a portfolio of risks
• Rating;
• Homogeneous and non-homogeneous risks;
• Facing portfolio riskiness;
• The uncertainty risk;
• Reinsurance;
• Alternative risk transfers;
• Securitisation and the role of capital markets;
• Premiums, payments, portfolio fund;
• Solvency and capital requirements.

Life Insurance
• Survival models and life contingencies;
• Survival distribution function;
• Life tables;
• Life insurance policies;
• Net single premium;
• Premium annuities.

Reserves
• Reserving methods;
• Formulas for some standard types of insurance;
• Recursive relations.

Pension plans

• Pension programs;
• Individual and group pension plans;
• Benefits and contributions;
• Pension savings before retirement;
• Retirement income;
• Life annuities.

Non-life insurance
• Non-life insurance products;
• Loss and claim amount;
• The equivalence premium;
• The expected aggregate claim amount;
• The net premium;
• The expense-loaded premium;
• Stochastic modeling of the aggregate claim amount;
• Risk classification and experience-rating;
• Technical reserves.

A. Olivieri, E. Pitacco, Introduction to Insurance Mathematics, Springer-Verlag; chapters 1, 2, 4, 5, 6, 7, 8, 9.

Grading is based on a final written exam, taken at the end of the course. This consists of 2 exercises to be solved and 10 closed-ended questions (duration: 2 hours). Each exercise accounts for 25% of the final grade of the exam; each question accounts for 5% of the final grade of the exam. The final grade will be the sum of the scores obtained in all exercises and questions.
The objective of the exercises is to test the student's ability to understand the computational aspects of the course and to apply them to compute the solution for a given problem. The objective of the closed-ended questions is to test the acquisition of the knowledge acquired and the ability to understand the insurance products studied.
The exam is closed-notes and closed-book, but students are allowed to use a pocket calculator. Students need to register for the exam in advance.

Lectures. Additional lecture notes and exercises will be available on the platform moodle.unive.it. Exercises will be assigned weekly to stimulate and test the acquisition of the knowledge and abilities on the topics covered during the week; students are expected to solve them regularly at home

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