Filtration F(t) for Girsanov's theorem and Martingale Representation Theorem

[kdmfe]

Dear experts,

I am reading Martingale Representation theorem from Steven Shreve's Stochastic Calculus book 2.

It is understood that Filtration F(t) for Martingale representation theorem is generated by Brownian motion, whereas for Girsanov's theorem filtration F(t) is generated for the Brownian motion.

I am not clear about the difference between the two filtration calculation methods, and also why this is significant for these two theorems.

Can anyone please refer me to any paper or a video which explains this.

I am reading Stochastic Calculus with the help of a Phd. student and my only sources of gaining understanding is forums like these.

Kindly help.

 

[Qui-Gon]

You are reading the wrong text if you care about what most people would consider the minutiae of stochastic calculus. Consider checking out Brownian Motion and Stochastic Calculus by Karatzas and Shreve.

Also, I would consider decreasing the frequency of your posts -- one does not learn mathematics by posting on a forum every time they have a question. Sometimes you need to consult multiple different sources, read and reread many times and think hard. The last point is the most important, and no, thinking hard does not mean thinking for 3 hours. I'm not saying you are not already doing this, but learning a subject like stochastic calculus rigorously takes endurance and stubborness. QuantNet is not a substitute for this.

 

[kdmfe]

Hello Qui-Gon,​

Thank you for time and the posts.

I searched on Amazon India and found a book (paper back) with the below title (yellow cover page)

​

Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) Paperback – 28 September 2004​

Buy Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) Book Online at Low Prices in India | Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) Reviews & Ratings - Amazon.in

Amazon.in - Buy Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) book online at best prices in India on Amazon.in. Read Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) book reviews & author details and more at Amazon.in. Free delivery on...

www.amazon.in

Is this the book you were referring to. Kindly help.

Please give me some more time to respond on your second para. But thank you anyway.

Thank you all once again.

 

[Qui-Gon]

Hello Qui-Gon,​

Thank you for time and the posts.

I searched on Amazon India and found a book (paper back) with the below title (yellow cover page)

​

Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) Paperback – 28 September 2004​

Buy Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) Book Online at Low Prices in India | Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) Reviews & Ratings - Amazon.in

Amazon.in - Buy Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) book online at best prices in India on Amazon.in. Read Brownian Motion and Stochastic Calculus: 113 (Graduate Texts in Mathematics) book reviews & author details and more at Amazon.in. Free delivery on...

www.amazon.in

Is this the book you were referring to. Kindly help.

Please give me some more time to respond on your second para. But thank you anyway.

Thank you all once again.

Yes, that is the book I was referring to.

 

[rajanS]

Lol useless subject.

 

[Qui-Gon]

Lol useless subject.

Perhaps for what you intend to get out of it. For someone interested in doing a PhD in mathematics focused on probability and stochastic analysis, absolutely not. Have you ever heard of Bruno Dupire or Julien Guyon? Hate to break it to you, but some of the most top-performing quants spent several hours learning "useless subjects". You seem like someone with a one-dimensional understanding and appreciation of quantitative finance, lol.

 

[kdmfe]

rajanS,

With due respect.

In our Sanatana dharma, there is no such thing as 'useless'. In ones own understanding, a thinking process has either taken a higher dimension of self-realisation or yet to take place/is in the process. Everything takes time.

I am new to Mathematics, and I am not a math student. I am an accountant. I took interest in understanding (not reading/studying) stochastic calculus.

I am not sure in what context you have made the above statement. I am not judging youi. Irrespective, your statement reflects poorly on you. A pity.

Are you sure to whom it has served any purpose? Are you able to expand on what and why you wrote. Please do not criticise, if you cannot add value or make something better.

Kindly use your productive hours to contribute any positive to anyone.

I for at least cannot read fictitious threads and waste my precious time and energy. So should be the same with most of us here.

I will welcome you to come forward and put forth you positive criticism.

I really hope that you will either withdraw your baseless statement or remain positive in your postings in future.

Wishing you all the very best.

 

[PepeQuant]

Lol useless subject.

This is quite ignorant.

I don't understand why you think this is useless unless you trade cash products all day. But Stoch Calc still has its place especially for equity derivatives. Check optiva and SIG.

Also the subject is very intellectually challenging some people do find it interesting.

 

[rajanS]

This is quite ignorant.

I don't understand why you think this is useless unless you trade cash products all day. But Stoch Calc still has its place especially for equity derivatives. Check optiva and SIG.

Also the subject is very intellectually challenging some people do find it interesting.

I work in cryptos. It’s useless in that field. I wouldn’t say it’s useless if you are doing pricing. Anything else, yes useless.

 

[PepeQuant]

I work in cryptos. It’s useless in that field. I wouldn’t say it’s useless if you are doing pricing. Anything else, yes useless.

that I agree

 

[Qui-Gon]

I work in cryptos. It’s useless in that field. I wouldn’t say it’s useless if you are doing pricing. Anything else, yes useless.

Stochastic calculus is not just useful in pricing. You speak from ignorance. Open a book on continuous time dynamic programming applied to finance. Stick to your knowledge base if you feel the need to opine on something.