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

Bibliography to self-study

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
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_U11+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UW P7S_WG
02	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
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+	P7S_KK P7S_WG
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+	P7S_KK P7S_UW P7S_WG
05	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

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	Random interest rate. Capital value as a random variable of the interest rate. Application of a log-normal random variable to model a random capital value. 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	Measures of risk associated with investing in shares. Standard deviation of the share return as a classic measure of risk. Semivariance and standard deviation of the rate of return. Average deviation of the rate of return. Probability of not reaching the aspiration level. Coefficient of variation of the return. Utility theory. 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)	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	The final grade is average from the exercises and the 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