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B028442 - STATISTICAL METHODS FOR QUANTITATIVE RISK MANAGEMENT
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Sustainable Development Goals 2030
Academic Year 2023-24
Coorte 2022 - Second Cycle Degree in STATISTICS AND DATA SCIENCE
Course year
Second year - First Semester
Belonging Department
Statistics, IT and its applications "G. Parenti" (DISIA)
Course Type
Single education field course
Scientific Area
SECS-S/01 - STATISTICS
Credits
9
Teaching Hours
72
Teaching Term
13/09/2023 ⇒ 07/12/2023
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Teaching Language
Italian
Course Content
Introduction to quantitative risk management. Probabilistic and statistical evaluation of risks. Elements of Extreme Value Theory. Statistical, financial and actuarial instruments for risk management.
Suggested readings (Search our library's catalogue)
1. P. Embrechts, R. Frey, A. McNeil – Quantitative Risk Management – Princeton University Press, 2015
2. P.J. Boland – Statistical and Probabilistic Methods in Actuarial Science – Chapman & Hall, 2011
3. P. Shevchenko - Modelling Operational Risk Using Bayesian Inference – Springer Verlag, 2011
2. P.J. Boland – Statistical and Probabilistic Methods in Actuarial Science – Chapman & Hall, 2011
3. P. Shevchenko - Modelling Operational Risk Using Bayesian Inference – Springer Verlag, 2011
Learning Objectives
How can a scholar of statistics, probability, actuarial science become a risk manger.? To this end the course wishes to provide both some instruments and some suggestions. The ultimate goal is to found an inventive and innovative practice on a solid and updated theoretical knowledge.
Prerequisites
Probability and Mathematics for Statistics.
Statistical Inference
Statistical Inference
Teaching Methods
Lectures and laboratories.
Further information
The goal of the course is to introduce the concept of risk in several contexts and activities (finance, insurance, health systems, environment etc.), so as to describe methods and models aimed to calculate a "risk price". That is, indeed, the specific competence of the actuarial profession: establishing a price for a risk. Howevere, such activity is connected to anotherone: managing a risk, mitigating, in particular, its consequences. To this end will be defined the extreme or catastrophic risks and financial-actuarial instruments will be illustrated, aimed at prevention and mitigation.
Type of Assessment
Intermediate tests and final examination: written and oral tests.
Course program
1. Introduction to Quantitative Risk Management.
a) Definition of economic risk. Finance and insurance risks: examples.
b) The concept of risk aversion. Risk premium and insurance prices. HARA utility functions. Numerical examples.
c) The loss variable. Loss distribution for a risk portfolio. Portfolios of stocks, options, bonds, risky credits.
d) Risk measures. Value at Risk and Expected Shortfall. Basel and Solvency guidelines. Computational method for risk measures: Monte Carlo simulations and deterministic algorithms.
2. Probabilistic and statistical evaluation of risks.
a) Aggregate distributions of risks and their approximation.
b) Bayesian inference for loss distributions.
c) Models of risk dependence. Copulas through statistical inference.
3. Elements of Extreme Value Theory
a) Extreme values topics.
b) Probabilistic and statistical models of extreme risks: light and heavy distributions of losses. The ruin probability in the two cases.
c) Limits of sums and maxima.
d) The Fisher-Tippet theorem.
e) Generalized Pareto distribution: numerical cases.
4. Statistical, financial and actuarial tools for risk management
a) Financial products for environment risk prevention and mitigation: CAT bonds and project options. Data analysis and case studies: floods, earthquakes, drought.
b) Statistical evaluation of health risks. Public health care and private insurance. The mal-practice risk. Defensive medicine, insurance and litigation: evolutionary models.
c) Art and heritage risk management. Role of foundations. Insurance policies and ethical finance.
a) Definition of economic risk. Finance and insurance risks: examples.
b) The concept of risk aversion. Risk premium and insurance prices. HARA utility functions. Numerical examples.
c) The loss variable. Loss distribution for a risk portfolio. Portfolios of stocks, options, bonds, risky credits.
d) Risk measures. Value at Risk and Expected Shortfall. Basel and Solvency guidelines. Computational method for risk measures: Monte Carlo simulations and deterministic algorithms.
2. Probabilistic and statistical evaluation of risks.
a) Aggregate distributions of risks and their approximation.
b) Bayesian inference for loss distributions.
c) Models of risk dependence. Copulas through statistical inference.
3. Elements of Extreme Value Theory
a) Extreme values topics.
b) Probabilistic and statistical models of extreme risks: light and heavy distributions of losses. The ruin probability in the two cases.
c) Limits of sums and maxima.
d) The Fisher-Tippet theorem.
e) Generalized Pareto distribution: numerical cases.
4. Statistical, financial and actuarial tools for risk management
a) Financial products for environment risk prevention and mitigation: CAT bonds and project options. Data analysis and case studies: floods, earthquakes, drought.
b) Statistical evaluation of health risks. Public health care and private insurance. The mal-practice risk. Defensive medicine, insurance and litigation: evolutionary models.
c) Art and heritage risk management. Role of foundations. Insurance policies and ethical finance.
Sustainable Development Goals 2030
1,2,3