Karta przedmiotu

Actuarial 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:

first degree study

Type of study:

full time

discipline specialities :

Applications of Mathematics in Economics

The degree after graduating from university:

bachelor's degree

The name of the module department :

Departament of Mathematical Modelling

The code of the module:

1062

The module status:

mandatory for teaching programme Applications of Mathematics in Economics

The position in the studies teaching programme:

sem: 6 / W30 C15 / 2 ECTS / Z

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:
To acquaint students with the basics of insurance mathematics and familiarize them with the simplest models of risk.

The general information about the module:
The module is implemented in the sixth semester. It consists of 30 hours of lectures and 15 hours of tutorials.

Bibliography required to complete the module

Bibliography used during lectures
1	P. Kowalczyk, E. Poprawska, W. Ronka-Chmielowiec	Metody aktuarialne	Wydawnictwo Naukowe PWN, Warszawa.	2006
2	T. Michalski, K. Twardowska, B. Tylutki	Matematyka w ubezpieczeniach, jak to wszystko policzyć	Wydawnictwo Placet, Warszawa.	2005

Bibliography used during classes/laboratories/others
1	S. Wieteska	Zbiór zadań z matematycznej teorii ryzyka ubezpieczeniowego	Wydawnictwo Uniwersytetu Łódzkiego,.	2001

Bibliography to self-study
1	A. Wiliams, H. Smith, P. Young	Zarządzanie ryzykiem a ubezpieczenia	Warszawa.	2002.

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. Zaloguj Zaloguj Zaloguj Zaloguj

Basic requirements in category social competences:
Willingness to take objectively justified mathematical operations in order to solve the task

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	student is able to give examples of random variables used in insurance risk theory: both discrete and continuous and to calculate the parameters of these variables	Lectures, classes	written test	K-U30+ K-U31+	P6S-UK P6S-UO P6S-UU P6S-UW
MEK02	knows the theoretical basis for the individual risk model, can determine the parameters of the aggregate claims distribution and uses the central limit theorems for estimating the probabilities	Lectures, classes	written test	K-W01+ K-W02+ K-W03+ K-W04+ K-U33+	P6S-UW P6S-WG P6S-WK
MEK03	knows the theoretical basis for the collective risk model, can determine the parameters of the aggregate claims dystribution	Lectures, classes	written test	K-W03+ K-U32+ K-U33+ K-U34+ K-K01+	P6S-KK P6S-UW P6S-WG P6S-WK
MEK04	can use the classic methods to calculate net premium	Lectures, classes	written test	K-U31+ K-U33+ K-K01+	P6S-KK P6S-UK P6S-UO P6S-UU P6S-UW

The syllabus of the module

Sem.	TK	The content	realized in	MEK
6	TK01	Probability: random variable, probability distribution, distribution function, the Riemann–Stieltjes integral, moments, conditional expectation, distribution of a sum of independent random variables., the moment-generating function, approximation for the distribution of sums of independent random variables. Selected probability distributions i) continuous: Pareto, lognormal, Weibull, uniform, exponential and ii) discrete: binomial, Poisson, negative binomial.	W01, W02, W03, W04, W05, C01, C02, C03	MEK01
6	TK02	Risk as a subject of insurance. Insurable and non-insurable risks. Types of risk : personal and estate, insurance risk measures, catastrophic risk. Individual risk models for short term. General assumptions and examples. Collective risk models for a single period.	W06, W07, W08, W9, W10, W11, C04, C05, C06	MEK01 MEK02 MEK03
6	TK03	Premium calculation principles: pure risk premium, premium with safety (security) loading.	W12, W13, W14, W15, C07, C08	MEK04

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 6)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 2.00 hours/sem.
Class (sem. 6)	The preparation for a Class: 3.00 hours/sem. The preparation for a test: 5.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Studying tasks: 2.00 hours/sem.
Advice (sem. 6)		The participation in Advice: 1.00 hours/sem.
Credit (sem. 6)		The written credit: 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 mean of grades obtained for two written tests. This grade may be increased if the student demonstrates the activity on the classes.
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

The contents of the module are associated with the research profile no