CREDIT RISK AND INSURANCE
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 credit risk and the risk arising in life insurance markets.
KNOWLEDGE AND UNDERSTANDING:
The course discusses the main deterministic and stochastic methord for modelling financial markets subject to default risk and life insurance markets, and pricing defaultable derivatives and 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 credit risk and life insurance contracts, and to indentify their main characteristics. Students will also be able to apply quantitative techniques for evaluating different types of contracts.
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.
The objective of this course is to understand the main mathematical techniques for the modelling and the analysis of credit risk and the risk arising in life insurance markets.
KNOWLEDGE AND UNDERSTANDING:
The course discusses the main deterministic and stochastic methord for modelling financial markets subject to default risk and life insurance markets, and pricing defaultable derivatives and 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 credit risk and life insurance contracts, and to indentify their main characteristics. Students will also be able to apply quantitative techniques for evaluating different types of contracts.
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
Financial mathematics (compound intereset rates, force of interest and annuities).
Probability (Discrete and continuous random variables, expectations, conditional probability)
Probability (Discrete and continuous random variables, expectations, conditional probability)
Program
1. Survival probability (4 hours)
2. Life Insurance contracts (6 hours)
3. Life Annuities (6 hours)
4. Net Premiums and Reserve Calculations (4 hours)
5. Equity linked and Unit linked Insurance (4 hours)
6. Modeling of default times (6 hours)
7. Valuation of defaultable contracts (6 hours)
2. Life Insurance contracts (6 hours)
3. Life Annuities (6 hours)
4. Net Premiums and Reserve Calculations (4 hours)
5. Equity linked and Unit linked Insurance (4 hours)
6. Modeling of default times (6 hours)
7. Valuation of defaultable contracts (6 hours)
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.
3. Quantitative Risk Management. McNeil A., Frey R. and Embrecht, P. 2nd ed. Princeton University Press
2. Actuarial Mathematics for Life Contingent Risks. David C. M. Dickson, Mary R. Hardy, Howard R. Waters. 3rd ed. Cambridge University Press, 2020.
3. Quantitative Risk Management. McNeil A., Frey R. and Embrecht, P. 2nd ed. Princeton University Press
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.
3. Quantitative Risk Management. McNeil A., Frey R. and Embrecht, P. 2nd ed. Princeton University Press
2. Actuarial Mathematics for Life Contingent Risks. David C. M. Dickson, Mary R. Hardy, Howard R. Waters. 3rd ed. Cambridge University Press, 2020.
3. Quantitative Risk Management. McNeil A., Frey R. and Embrecht, P. 2nd ed. Princeton University Press
Teaching methods
Theoretical lectures and exercises
Exam Rules
Learning will be verified through a written exam where you will be asked to solve exercises and to answer theoretical questions on all topics covered during letures.
The exam is passed if the written test is evaluated 18/30 or more. If the exam is passed (i.e. the mark in the written test is at least 18/30), you can withdraw and repeat the exam in one of the next exam calls. This can be done ONE TIME ONLY. The mark obtained at the next exam date cancels the previous mark and cannot be rejected.
To pass this exam 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, describe them in mathematical terms and provide their financial meaning; 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.
Criteria for Formulating the Grade Out of Thirty:
Not sufficient: Significant deficiencies and/or inaccuracies in the knowledge and understanding of the topics; limited analytical and synthesis skills, frequent generalizations.
18-20: Barely sufficient knowledge and understanding of the topics with possible imperfections; sufficient analytical, synthesis, and judgment autonomy skills.
21-23: Routine knowledge and understanding of the topics; correct analytical and synthesis skills with coherent logical argumentation.
24-26: Fair knowledge and understanding of the topics; good analytical and synthesis skills with arguments expressed with sufficient mathematical and economic/financial rigor.
27-29: Complete knowledge and understanding of the topics; considerable analytical and synthesis skills. Good judgment autonomy and arguments expressed with good mathematical and economic/financial rigor.
30-30L: Excellent level of knowledge and understanding of the topics. Remarkable analytical, synthesis, and judgment autonomy skills. Arguments expressed with excellent mathematical and economic/financial mastery.
The exam is passed if the written test is evaluated 18/30 or more. If the exam is passed (i.e. the mark in the written test is at least 18/30), you can withdraw and repeat the exam in one of the next exam calls. This can be done ONE TIME ONLY. The mark obtained at the next exam date cancels the previous mark and cannot be rejected.
To pass this exam 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, describe them in mathematical terms and provide their financial meaning; 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.
Criteria for Formulating the Grade Out of Thirty:
Not sufficient: Significant deficiencies and/or inaccuracies in the knowledge and understanding of the topics; limited analytical and synthesis skills, frequent generalizations.
18-20: Barely sufficient knowledge and understanding of the topics with possible imperfections; sufficient analytical, synthesis, and judgment autonomy skills.
21-23: Routine knowledge and understanding of the topics; correct analytical and synthesis skills with coherent logical argumentation.
24-26: Fair knowledge and understanding of the topics; good analytical and synthesis skills with arguments expressed with sufficient mathematical and economic/financial rigor.
27-29: Complete knowledge and understanding of the topics; considerable analytical and synthesis skills. Good judgment autonomy and arguments expressed with good mathematical and economic/financial rigor.
30-30L: Excellent level of knowledge and understanding of the topics. Remarkable analytical, synthesis, and judgment autonomy skills. Arguments expressed with excellent mathematical and economic/financial mastery.