Introduction to Stochastic Calculus & Application in Finance

HKUST?

遲啲有時間借黎睇先

呢個concept真係好神奇
同埋我都幾肯定如果我依家係財經台同買緊動物啲人講呢樣嘢
佢肯定會覺得我痴撚咗線

馬料水

神帖lm

留名
下個sem讀stochastic process

Stochastic process同stochastic calculus係唔同
我呢個post其實冇點分析過stochastic process本身嘅property
而stochastic process本身已經有幾種
一開始你應該會學discrete time & discrete state space 嘅 discrete stoc. process
然後再generalize上去就係continuous time but discrete state space 嘅 continuous-time stoc. process
最後就係continuous time & continuous state space 嘅 continuous stoc. process

而我呢篇文其實只係用緊其中一個continuous stoc. process 亦都係當中最簡單嗰個
就係wiener process 佢嘅property我都只係喺一開頭略略提過

想做quant唔好番香港

原來係咁
辛苦曬打咁長嚟解釋

可能係原proof
不過識得martingale個proof就夠啦

應該去邊好？巴打你做Quant？

It is very important NOT to confuse the proof for Feynman Kac formula in QFT as the “real” proof. As the two integrals in QFT and Stochastic Calculus are defined differently.

都係嘅
如果夠位嘅話我section 3最尾會做一次martingale嗰個proof
不過應該會簡化少少嘢 唔會寫得太formal
(其實上面嗰堆嘢我好多都寫得唔formal )

呢個真係長知識
多謝巴打指正

No worries, many physicists and engineers make this mistake as well by treating the Wiener path integrals as stochastic integrals. I recently just saw a few engineers making this mistake in their paper when I was a referee for a journal.

Although numerically they are often the same, conceptually they are very different as stochastic integral is defined in a L2 sense. It is not possible to define it path by path as a Lebesgue Stieljes integral since the Brownian motion paths are of infinite variation almost surely.

Were you guys taught how to define stochastic integrals in your course?

Yes but in a later stage. There is a separate course that really teaches us stochastic calculus formally, the 1st half of it is pretty much like a real analysis course, but for now we are only up to conditional expectation.
(Btw now you've mentioned Lebesgue Stieljes integral, I seem to understand why they are different )

The content I'm using here actually came from another course, the nature of that course is kind of like "Application of stochastic calculus in Finance", so that's why it's a bit informal.
But I think it's already good enough to serve as the backbone of this post.

所以我一直追問另一位巴打咩叫"真正"的proof...

淨係random variable 個definition
對於non math major 既人真係幾難明
無學過d notation

Linear Algebra有咩好書介紹

呢個真係我錯
undergrad才疏學淺

No problem. It’s indeed very nice that you are giving a concise introduction to the applications of stochastic calculus in finance. I find them very helpful.

I am also trying to learn some mathematical finance as I will be looking for job very soon and don’t have any background in finance. I was reading a book called “The Concepts and Practice of Mathematical Finance” by Mark Joshi. I have also heard the book by Wilmott is good.

And sorry I can’t tell you guys more about the Feynman path integrals as I’m not an expert in QFT. My knowledge of physics is rather limited, my undergrad major was pure maths and I did some physics only up to 3rd year undergrad. My current research focuses on stochastic differential equations that’s why I’m also thinking about working as a quant.

What course are you doing and where are you doing it?

lm

以呢個唔太重視基本 mathematical analysis 既 undergrad program 黎講，樓主已經寫得好唔錯啦

我唔係quant

簡單講下sell side quant既分類，概括都可分為front/middle/back office

fo quant主要都係幫trading desk開發model或者分析exotic deriv risk
middle to back就會做xva/valuation/model validation

fo quant香港機會始終唔太多，主要係鬼佬玩晒(唔少係法國人)。model validation既機會就好少少，銀行或者consultant都會請。但始終都係fo quant搵得多啲

你有冇phd，好多fo quant都係拎住個phd

buy-side方面就唔太清楚，等其他巴打補充