Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Hi Guys,

Just wondering if you could suggest applications of distribution of the supremum of a fractional Brownian motion process with a drift ?

Also if you could possibly recommend how to approach this problem, that would be much appreciated.

Cheers

share|improve this question
    
Where does this question come from? If you know what a fractional BM with drift is, then why not try to study the distribution of its supremum? (I assume you mean the process $Y_t = \sup_{o\leq s\leq t} X_s$.) I really don't understand what you mean by "application" and "project" –  Yemon Choi Feb 8 '12 at 0:39
    
Firstly thanks for your reply. My question was mearly to find out where such a distribution could be used in real world. I am an honours student and i am considering this as a thesis project, i was told that this is an old unsolved problem but was never given any motivation behind this project. I am just trying to fill in some blanks here. If you share your suggestions or knowldege it would be much appreciated. –  Hardy Feb 8 '12 at 2:14
add comment

1 Answer

up vote 4 down vote accepted

An application that springs to mind immediately is option evaluation. Suppose I offer you to buy a contract to me: after three months I pay you the maximum value of the price of an asset. How much are you willing to pay this contract ? If you model the price of the assert by a drifted brownian motion, then you'll probably want to estimate the distribution of this maximum and take the expected value as a first guess of this maximum price. This will also be my first guess at the minimum price at which I will be willing to sell the contract. This is a non arbitrage price.

Note to purists : of course one will object that each of the parties can hedge himself, and that the distribution has to be corrected by a risk neutral argument (which will probably discard the initial drift and replace it by a zero risk rate drift instead).

N.b. : this is a real world application, exotic option traders buy and sell like contracts everyday.

share|improve this answer
    
Thanks so very much mate. You are a Rock Star. –  Hardy Feb 15 '12 at 6:57
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.