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
錦衣衞
2018-10-28 02:03:30
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.
錦衣衞
2018-10-28 02:24:24
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?
宇智波月巴
2018-10-28 02:46:44
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.
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(Btw now you've mentioned Lebesgue Stieljes integral, I seem to understand why they are different
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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.
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But I think it's already good enough to serve as the backbone of this post.
tyuonb
2018-10-28 14:53:49
淨係random variable 個definition
對於non math major 既人真係幾難明
無學過d notation
薯餅
2018-10-28 14:59:37
Linear Algebra有咩好書介紹
宇智波月巴
2018-10-28 15:00:17
呢個真係我錯
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undergrad才疏學淺
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錦衣衞
2018-10-28 17:33:12
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.
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錦衣衞
2018-10-28 17:35:16
What course are you doing and where are you doing it?
醉愛乂碎少
2018-10-28 18:32:41
lm
左頌星
2018-10-28 21:59:52
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
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S.Lev
2018-10-28 23:33:31
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