Courses in Stochastics in Autumn 2009
Eija Laukkarinen
Lévy-prosessit (Lévy Processes)
MATS275, 4 op, 24 h
Time and Place
| Wednesday |
: |
08-10 MaD 381 |
| Thursday |
: |
08-10 MaD 380 |
| First lecture |
: |
16/09/2009 |
Description:
Äkillisiä muutoksia tapahtuu. Esimerkiksi osakkeiden hinnoissa esiintyy rajujakin hyppyjä.
Brownin liike on eniten tutkittu stokastinen prosessi, mutta sillä voidaan mallintaa täydellisesti
vain ilmiöitä, joissa muutokset ovat jatkuvia eli hyppyjä ei ole. Lévy-prosessit sallivat hypyt,
mutta säilyttävät joitakin niistä Brownin liikkeen ominaisuuksista, jotka tekevät siitä niin suositun
ja hyödyllisen. Kurssilla tutustutaan Lévy-prosessien jakaumaan ja hyppyjen luonteeseen.
Rapid changes do occur. For instance in stock prices there can even be fierce jumps. The Brownian
motion is the most studied stochastic process, but it can model perfectly only phenomena where
changes happen continuously meaning there are no jumps. Lévy processes allow jumps, but retain some
of the properties of the Brownian motion that make it so popular and useful. We study the distribution
and nature of jumps of Lévy processes.
Literature
- D. Applebaum:
Lévy processes and Stochastic Calculus (Cambridge)
- K. Sato:
Lévy processes and Infinitely Divisible Distributions (Cambridge)
Exercises, lecture notes and information
Christel Geiss
Stokastiset mallit
(Stochastic Modeling)
MATA271, 4op 28h
Time and Place:
Monday 12-14 MaD 381
Tuesday 14-16 MaD 381
First lecture: 07/09/2009
Description: The financial market is
as unpredictable as the weather! Nevertheless, there are mathematical
models to describe and understand both of them better. Starting
with random walk to model stock prices
and the weather, we arrive
at the theory of Markov chains. We continue with simple applications of
Markov chains in genetics and finally come to Markov Chain Monte
Carlo methods.
Literature:
[1] P. Guttorp: Stochastic
Modeling of Scientific Data
(Chapman & Hall)
[2] O. Häggström: Finite
Markov Chains and Algorithmic Applications
[3] Wai-Yuan Tan: Stochastic
Models with Applications to Genetics, Cancers,
AIDS and Other Biomedical Systems
Script
Video
Notes from the videos
Lecture1
Lecture2
Lecture3
Lecture4
Lecture5
Lecture6
Lecture7
Lecture8
Lecture9
Lecture10
Lecture11
Lecture12
Lecture13
Lecture14
Information:
Exercises:
15/09/2009
22/09/2009
29/09/2009
06/10/2009
13/10/2009
20/10/2009
27/10/2009
Topics for the test
Christel Geiss
Vakuutusmatematiikkaa
(Non-Life Insurance Mathematics)
MATA275, 3 op (2 ov) 20h
Time
and Place:
Monday 12-14 MaD 381
Tuesday 14-16 MaD 381
First lecture: 26/10/2009
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.
Script