Courses in Stochastics in Autumn 2006




Christel Geiss

Rahoitusteorian stokastisia malleja
(Models in Financial Mathematics)
MATA272,  5 op (3 ov)

Time and Place:
Monday    12-14 MaD 381
Tuesday   14-16 MaD 381

First lecture: 11/09/2006 

Description: Does Probability Theory help to make money at the
stock exchange? If you would like to know this you are welcome to
the course: after introducing some basic probabilistic methods one
can already start to investigate market models. We will compute

-) fair prices for European and American options,
-) explain what hedging is from a mathematical point of view,
-) find out whether hedging of an option is always possible.

Literature:
R. Elliott, P. Kopp: Mathematics of Financial Markets
D. Lamberton, B. Lapeyre: Stochastic Calculus Applied to Finance

Exercises :

Problems 19/09/2006
Problems 26/09/2006
Problems 03/10/2006
Problems 10/10/2006
Problems 17/10/2006
Problems 24/10/2006
Problems 31/10/2006
Problems 07/11/2006
 
Stefan Geiss

Probability Theory 2
MATS261, 5ov (9 op), 50 h

Time and Place:
Wednesday     8-10 MaD 381
Thursday      8-10 MaD 380

First lecture: 06/09/2006

Description:  Doing computations for experiments one
often ends up with sums of independent random variables
and is interested in their limit distributions. Why do
we get sometimes a constant as limit and sometimes a
Gaussian random variable? Are there other possibilities?
But before: in what sense does the convergence take place?
To give an answer to part of these questions we use
Characteristic Functions, an important tool in probability.

Contents of the lecture:
 1. Modes of convergence of random variables
 2. Characteristic functions of random variables
 3. Limit distributions

Literature:
[1] H. Bauer: Probability Theory (de Gruyter)
[2] A.N. Shiryaev: Probability (Springer)

Script:

Exercises:
Problems 14/09/2006
Problems 21/09/2006
Problems 28/09/2006
Problems 05/10/2006
Problems 12/10/2006
Problems 19/10/2006
Problems 26/10/2006
Problems 02/11/2006
Problems 09/11/2006
Problems 16/11/2006
Problems 23/11/2006
Problems 30/11/2006


 
Christel Geiss

Vakuutusmatematiikkaa
(Non-Life Insurance Mathematics)
MATA275,  2 op (1 ov)

Time and Place:
Monday    12-14 MaD 381
Tuesday   14-16 MaD 381

First lecture: 13/11/2006 

Description: Insurance against theft, car damage, fire - how
to compute the amount one should pay for this? This question
leads to the so called risk theory. Poisson processes and more
general renewal processes will be introduced to model the risk
and estimate the ruin probability.

Literature:
T. Mikosch: Non-Life Insurance Mathematics

Exercises :

Problems 21/11/2006
Problems 28/11/2006
 Problems 05/12/2006