Item card
Probabilistic aspects of financial and insurance mathematics
Some basic information about the module
Cycle of education:
2019/2020
The name of the faculty organization unit:
The faculty Mathematics and Applied Physics
The name of the field of study:
Mathematics
The area of study:
sciences
The profile of studing:
The level of study:
second degree study
Type of study:
full time
discipline specialities :
Applications of Mathematics in Economics
The degree after graduating from university:
master
The name of the module department :
Departament of Mathematical Modelling
The code of the module:
1491
The module status:
mandatory for teaching programme Applications of Mathematics in Economics
The position in the studies teaching programme:
sem: 3 / W30 C30 / 5 ECTS / E
The language of the lecture:
Polish
The name of the coordinator:
Liliana Rybarska-Rusinek, DSc, PhD
office hours of the coordinator:
podane w harmonogramie pracy jednostki.
The aim of studying and bibliography
The main aim of study:
Students should have the knowledge and skills of modeling some financial and insurance phenomena by using probabilistic methods.
The general information about the module:
The module is implemented in the third semester. It consists of 30 hours of lectures and 30 hours of tutorials.
Bibliography required to complete the module
| 1 | N. Bowers, H. Gerber, J. Hickman, D. Jones, C. Nesbitt | Actuarial Mathematics | The Society of Actuaries. | 1986 |
| 2 | K. Jajuga, T. Jajuga | Inwestycje: instrumenty,finansowe, aktywa niefinansowe, ryzyko finansowe, inżynieria finansowa | PWN, Warszawa . | 1999 |
| 3 | J. Jakubowski, A. Palczewski, M. Rutkowski, Ł. Stettner | Matematyka finansowa | Wydawnictwa Naukowo-Techniczne, Warszawa . | 2003 |
| 1 | M. Podgórska, J. Klimkowska | Matematyka finansowa | PWN, Warszawa . | 2005 |
| 1 | 1. N. Bowers, H. Gerber, J. Hickman, D. Jones, C. Nesbitt | Actuarial Mathematics | The Society of Actuaries. | 1986 |
Basic requirements in category knowledge/skills/social competences
Formal requirements:
The student satisfies the formal requirements set out in the study regulations
Basic requirements in category knowledge:
Basic knowledge in fields of probability and statistics.
Basic requirements in category skills:
Ability to use the basic mathematical apparatus for the probability and statistic.
Basic requirements in category social competences:
Ability of individual and group learning, awaresness of the level of own knowledge and awaresness of necessity of self-education.
Module outcomes
| MEK | The student who completed the module | Types of classes / teaching methods leading to achieving a given outcome of teaching | Methods of verifying every mentioned outcome of teaching | Relationships with KEK | Relationships with PRK |
|---|---|---|---|---|---|
| MEK01 | knows the random variables used in financial mathematics for modeling present/future value (random interest and discount rates). | Lectures, classes. | written test |
K-W04+ K-W07+ K-W08+ K-W09+ K-U11+ K-K07+ |
P7S-KK P7S-KO P7S-KR P7S-UW P7S-WG |
| MEK02 | is able to analyze the income and risk of investments, knows the theoretical bases of the portfolio theory of two and many companies and the theory of the portfolio, taking into account risk-free instruments, is able to designate a minimum risk portfolio, an effective portfolio with a given rate of return. | Lectures, classes | written test |
K-W09+ K-U02+ K-U04+ K-U12+ K-U16+ K-K02+ |
P7S-KK P7S-KO P7S-UK P7S-UO P7S-UU P7S-UW P7S-WG |
| MEK03 | knows simple models of capital market equilibrium: single index model, capital asset pricing model CAPM, arbitrage pricing theory APT. | Lectures, classes | written test |
K-W09+ K-K01+ |
P7S-KK P7S-WG |
| MEK04 | is able to calculate the net single premium for simple life insurances (using International Actuarial Notation , life-table and theory of Interest) | Lectures, classes | written test |
K-W09+ K-U12+ K-K01+ |
P7S-KK P7S-UW P7S-WG |
| MEK05 | knowns the option pricing models: binomial and Black-Scholes. | lectures, classes | written test |
K-W09+ K-U18+ K-K01+ K-K03+ K-K04+ |
P7S-KK P7S-KO P7S-KR P7S-UW P7S-WG |
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 3 | TK01 | W01, W02, W03, W04, W05, C01, C02, C03, C04, C05 | MEK01 MEK05 | |
| 3 | TK02 | W06, W07, W08, W09, C06, C07, C08, C09 | MEK02 | |
| 3 | TK03 | W10, W11, C10, C11 | MEK03 | |
| 3 | TK04 | W12, W13, W14, W15, C12, C13, C14, C15 | MEK04 |
The student's effort
| The type of classes | The work before classes | The participation in classes | The work after classes |
|---|---|---|---|
| Lecture (sem. 3) | The preparation for a test:
10.00 hours/sem. |
contact hours:
30.00 hours/sem. |
complementing/reading through notes:
5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem. |
| Class (sem. 3) | The preparation for a Class:
10.00 hours/sem. The preparation for a test: 10.00 hours/sem. |
contact hours:
30.00 hours/sem. |
Finishing/Studying tasks:
10.00 hours/sem. |
| Advice (sem. 3) | The preparation for Advice:
10.00 hours/sem. |
The participation in Advice:
3.00 hours/sem. |
|
| Exam (sem. 3) | The preparation for an Exam:
10.00 hours/sem. |
The written exam:
2.00 hours/sem. |
The way of giving the component module grades and the final grade
| The type of classes | The way of giving the final grade |
|---|---|
| Lecture | Presence on lectures. |
| Class | The grade is the everage of grades (positive) obtained for two written tests |
| The final grade |
Sample problems
Required during the exam/when receiving the credit
(-)
Realized during classes/laboratories/projects
(-)
Others
(-)
Can a student use any teaching aids during the exam/when receiving the credit : no