about me
game theory
... more
Subscribe Weblog

By far, the most interesting stochastic process used in financial economics is Brownian motion. The role of Brownian motion in stochastic processes is similar to that of Normal random variables in elementary statistics. The concept of a random walk, the discrete counterpart of the (continuous time) Brownian motion, is well known among students of economics, since most macroeconomic time series behave in a similar fashion (A random walk is a special case of what is known as unit root process or I(1) process). The plot given below shows trajectories (realizations) of a random walk process.
Common knowledge: The Brownian movement was discovered in 1827 by Robert Brown, a botanist. While he was studying microscopic live, he noticed little particles of plant pollens jiggling around in the liquid he was looking at in the microscope, and he was wise enough to realize that these were not living, but were just little pieces of dirt moving around in the water. In fact he helped to demonstrate that this had nothing to do with life by getting from the ground an old piece of quartz in which there was some water trapped. It must have been trapped for millions and millions of years, but inside he could see the same motion. What one sees is that very tiny particles are jiggling all the time. This was later proved to be one of the effects of molecular motion, and we can understand it qualitatively by thinking of a great push ball on a playing field, seen from a great distance, with a lot of people underneath, all pushing the ball in various directions. We cannot see the people because we imagine that we are too far away, but we can see the ball, and we notice that it moves around rather irregularly. [1] (Java Applet demonstrating 2-d Brownian motion).

In most financial calculus books Norbert Wiener and Albert Einstein are mentioned as the guys who provided the mathematical foundation for the theory of random motions. Of further historical interest is the fact that in his thesis, Théorie de la Spéculation, Bachelier (1900) proposed the Brownian motion as a model for stock prices*. In Bachelier's time, Paris was the centre of speculation in bonds and he reasoned that increments of stock prices should be idendependent and normally distributed. Since at that time any mathematical theory of the stock market was beneath the dignity of "real" mathematicians (his mentor was Henri Poincaré), Bachelier's work never received much attention.

WHAT YOU DID NOT KNOW: The earliest attempt to model Brownian motion mathematically can be traced to T.N. THIELE of Copenhagen, who effectively created a model of Brownian motion while studying time series in 1880 !!(Sur la compensation de quelques erreurs quasi-systématiques par la méthodes de moindre carrés, Reitzel, Copenhagen)[2]. Go to this site to download a copy of "Aspects of T.N. Thiele's contributions to statistics." (Bulletin of the International Statistical Institute).

*stock prices are often assumed to follow geometric Brownian motion, which is the same as saying that the logs of stock prices follow a random walk with drift.

[1] The Feynman Lectures on Physics, 1977, Volume 1
[2]"A Short history of Stochastic Integration and Mathematical Finance" by Robert Jarrow and Philip Protter.

R-code: randomwalk (txt, 0 KB)
1stl meinte am 6. May, 17:55:
useR! 2004 - The R User Conference
Da du offensichtlich ein Fan von R bist, wollte ich dich auf die R User Conference aufmerksam machen.

Mahalanobis antwortete am 6. May, 19:16:
Hätte mich damals
fast angemeldet, aber da mein R-Wissen noch sehr bescheiden ist, waren mir die 150 Euro (mittlerweile 200 Euro) einfach zu viel. Trotzdem, danke für den Tipp! 
1stl antwortete am 6. May, 19:36:
teurer spaß
oh, dass der spaß was kostet hab ich noch nicht bemerkt. hab gedacht, man kann sich die vorträge einfach so anhören, genau wie bei der Jahrestagung der Nationalökonomischen Gesellschaft (NÖG) an der WU. 
Mahalanobis antwortete am 6. May, 20:35:
Bei meinem letzten Aufenthalt in Barcelona lief grad eine Microsoft-Conference - dort durfte man satte 1000 Euro auf den Tisch legen. Wennst auf eine Konferenz gehst, die auch nur entfernt in den Bereich Investmentbanking fällt, dann zahlst mind. 2000 Euro...

Teuer ist die R-Conference nur für jene, die noch mit den Basics kämpfen und mit einer "schaumamal"-Einstellung hingehen würden ;-D. 
kimcil (guest) antwortete am 7. Apr, 12:31:
I am preparing a research paper and collecting information on this topic. Your post is one of the better that I have read. Thank you for putting this information into one post.
alfamart official partner merchandise fifa piala dunia brazil 2014
Unit Link Terbaik di Indonesia Commonwealth Life Investra Link 
Ahmad (guest) antwortete am 16. Apr, 06:08:
If you think homeschooling is not a good option for you, you should rethink your approach. Homeschooling has grown in popularity over the last several years, and there are plenty of resources available to the homeschool teacher. latestedunews 
Ahmad (guest) antwortete am 16. Apr, 06:09:
Functional skills are a group of qualifications that have been developed by the government in the UK which are part of an initiative to improve the whole country’s numeracy, literacy and ICT skills. edu-essay 
begedir antwortete am 4. May, 19:22:
oh, dass der spaß was kostet hab ich noch nicht bemerkt. hab gedacht, man kann sich die vorträge einfach so anhören, genau wie bei der Jahrestagung der Nationalökonomischen Gesellschaft (NÖG) an der WU. cara belajar bahasa inggris dengan cepat , pengen cepat hamil , kata kata minta maaf 
davidpool antwortete am 14. May, 12:47:
Use the inside the foot to be able to kick the particular ball in order to improve quick passing. This will allow you to increase the space you can easily kick the particular ball more. 4sportsinjurycenters.com 
davidpool antwortete am 14. May, 12:47:
Practice dribbling along with your weak hand in terms of dribbling. Tie the dominant hand for the rear of one's back and also force oneself only utilize your weakened hand. pgesports.com 
davidpool antwortete am 14. May, 12:47:
Even when you’re not necessarily the staff prodigy, it is possible to outsmart the opponent simply by learning all you could can in regards to the game. Use the human brain power to be able to beat your competitors. brazosportsanctuary.com 
davidpool antwortete am 14. May, 12:48:
One regarding football gear will be the things you ought to already realize is that you might want shoulder parts. Ensure your shoulder parts fit is prior to hitting the particular field. They need to stay put rather than be inside great problem. hamilton-motorsport.com 
davidpool antwortete am 14. May, 12:48:
In bottom line, many folks nowadays provide an iphone. In the event you weren’t sure the way to use an individual iphone or perhaps whether you wished to buy a single, hopefully an individual learned from your article previously mentioned. moddingcomputers.com 
maskodok meinte am 15. Jan, 01:10:
Interesting topic for a blog. I have been searching the Internet for fun and came upon your website. Fabulous post. Thanks a ton for sharing your knowledge! It is great to see that some people still put in an effort into managing their websites. I'll be sure to check back again real soon.
Mobil Sedan COrolla,IDrpoker.com agen Texas poker Online Indonesia Terpercaya, Mobil Sedan COrolla, Cipto Junaedy 
ashleydanielle (guest) meinte am 1. May, 13:25:
I think
I found this is an informative and interesting post so i think so it is very useful and knowledgeable. I would like to thank you for the efforts you have made in writing this article.
ashleydanielle (guest) meinte am 1. May, 15:30:
I think
Thanks for sharing excellent informations. Your web-site is very cool. I'm impressed by the details that you have on this web site. It reveals how nicely you perceive this subject. Bookmarked this web page, will come back for extra articles. You, my pal, ROCK! I found simply the information I already searched all over the place and simply couldn't come across. What a perfect web-site.
URL Opner 
ttlwu meinte am 24. May, 16:41:
I think
I really impressed after read this because of some quality work and informative thoughts . I just wanna say thanks for the writer and wish you all the best for coming!.
blood pressure solution examples 
ttlwu meinte am 5. Jun, 11:18:
I think
Im no expert, but I believe you just made an excellent point. You certainly fully understand what youre speaking about, and I can truly get behind that.
text the romance back review 
ttlwu meinte am 16. Jul, 13:36:
I think that thanks for the valuabe information and insights you have so provided here.
Clicking Here 
thscp1122 meinte am 17. Jul, 12:01:
Interesting and amazing how your post is! It Is Useful and helpful for me That I like it very much, and I am looking forward to Hearing from your next..
more helpful hints