Mathematical Models of Risk and Their Applications

See semester study programme.

The course shall provide students with the knowledge of mathematical models and methods used in practice for assesment of insurance and financial risks. Students shall be able to apply mathematical models and methods to quantify risk of financial and insurance institutions, and be aware of advantages and disadvantage of the models/methods applied. Additionally, students shall master certain concepts in probability theory, like moment generating functions, cumulant generating functions, conditional expectation and conditional variance. The course consists of several lectures on probability methods and theoretical foundations of quantitative risk models with examples of their applications. The course provides a starting point for studying more advanced topics in actuarial science and financial engineering. The prerequisite of the course is the good knowledge of calculus and foundations of probability theory encompassing the notion of discrete and continuous random variables.

Literatura podstawowa:

1. R.Kass, M.Goovaerts, J.Dhaene, M.Denuit, Modern Actuarial Risk Theory - Using R, Springer, 2008;

2. A..J.McNeil, R. Frey, P. Embrechts, Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton University Press, 2021.

Literatura uzupełniająca:

Artykuły z czasopism: Mathematical Finance, Finance and Stochastics, Insurance: Mathematics and Economics

Wiedza:

Students after the course shall be able to:

1. describe risk using the concept of random variable and its distribution,

2. enumerate discrete and continuous probability distributions, commonly used for quantitative description of risk,

3. give examples of applications of discrete and continuous probability distributions,

4. provide examples of premium calculation principles and their properties,

5. provide examples of measures of risk and their properties,

6. characterize Value-at-Risk and Expected Shortfall,

7. describe the idea of Monte Carlo simulation methods,

8. describe the assumptions underlying collective risk model,

9. name the approximations used for loss distributions.

Umiejętności:

Students after the course shall be able to:

1. propose a suitable probability distribution for description of selected risks,

2. calculate key characteristics of selected probability distributions,

3. apply moment generating functions and cumulant generating functions in actuarial calculations,

4. calculate premiums and other actuarial quantities in insurance risk models,

5. apply various approximations to calculate VaR in risk models.

Kompetencje społeczne:

Students shall:

1. realize the necessity and possibility of managing risk as an indispensable element of activity of enterprises and financial institutions,

2. understand advantages and disadvantages of quantitative methods and models in insurance and finance.

egzamin tradycyjny-pisemny: 70.00%

inne: 30.00%