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
01	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
02	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
03	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
04	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

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

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	The final grade is the grade for knowledge obtained in classes

Sample problems

Required during the exam/when receiving the credit
Przykładowe_kolokwium.pdf

Realized during classes/laboratories/projects
Przykładowe_zadania_cw.pdf

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