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

Bibliography used during lectures

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

Bibliography used during classes/laboratories/others

1

M. Podgórska, J. Klimkowska

Matematyka finansowa

PWN, Warszawa .

2005

Basic requirements in category knowledge/skills/social competences

Formal requirements: Requirements accordant with Rules and Regulations of studies

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: Awareness of the level of knowledge, ability to learn individually and in groups

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 OEK
01	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_U02+ K_U11+ K_K07+	X2A_W02 X2A_W03 X2A_W04 X2A_W05 X2A_U01 X2A_U03 X2A_U05 X2A_K06
02	knows the concepts of Modern Portfolio Theory (risk and expected return, determining the efficient set, choosing the best portfolio).	Lectures, classes	written test	K_W09+ K_U02+ K_U04+ K_U12+ K_U16+ K_K02+ K_K04+	X2A_W03 X2A_W04 X2A_U01 X2A_U02 X2A_U03 X2A_U05 X2A_U06 X2A_K01 X2A_K02 X2A_K03 X2A_K04
03	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+ K_K02+	X2A_W03 X2A_W04 X2A_K01 X2A_K02
04	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+ K_K03+	X2A_W03 X2A_W04 X2A_U01 X2A_K01 X2A_K02 X2A_K05 X2A_K06 X2A_K07
05	knowns the option pricing models: binomial and Black-Scholes.	lectures, classes	written test	K_W09+ K_U04+ K_U12+ K_U18+ K_K01+ K_K03+	X2A_W03 X2A_W04 X2A_U01 X2A_U02 X2A_U03 X2A_U06 X2A_K01 X2A_K02 X2A_K05 X2A_K06 X2A_K07

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
3	TK01	The basic properties of the lognormal distributions. The present value (the future value) of money under random rates of interest (discrete and continuous compound interest). Derivative securities (forward contracts and futures, swap, options)	W01, W02, W03, W04, W05, C01, C02, C03, C04, C05	MEK01 MEK05
3	TK02	Classic and modern measures of investment risk. Modern portfolio theory. Expected utility theory.Stochastic dominance and optimal portfolio.	W06, W07, W08, W09, C06, C07, C08, C09	MEK02
3	TK03	Simple models of capital market equilibrium: single index model, capital asset pricing model CAPM, arbitrage pricing theory APT.	W10, W11, C10, C11	MEK03
3	TK04	The individual risk model and the collective risk model . The determination of the net single premium of various life insurance.	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)		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: 5.00 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 final mark is the mean of marks obtained for written tests
The final grade	The final mark is the mean of mark for knowledge obtained in classes and written exam

Sample problems

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

Realized during classes/laboratories/projects
Cwiczenia_przykładowe.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