Introduction to Stochastic Calculus & Application in Finance

其實讀呢科洗唔洗讀左ODE/PDE先，我minor math想遲D揀來讀
我見呢科係會用到ODE/PDE，但又prerequisite就凈係得probability

如果你對ode有基本嘅認知其實都已經讀到
點solve pde其實都唔太需要知
因為上堂我地見到嘅pde其實黎黎去去都係嗰一兩個form
你只要知道嗰一個form應該try啲咩樣嘅solution就ok
通常做到最尾都係由pde變兩條ode

咁當然你本身讀過ode/pde course再讀4007會更加輕鬆

實際linear interpolation已經夠用

留名
學校教到一舊舊

girsanov theorem有教ar用黎講點轉risk neutral measure, 不過你講其他個d都冇教

如果Girsanov Thm只係教點樣由P轉Q 其實只係教咗呢個Thm嘅一半
呢個Thm最強大嘅地方係我地可以由Q再轉去另一啲measure Q*
轉完之後就會簡化咗我地本來計緊under Q嘅expectation
我遲啲講到就會比啲例子大家

可唔可以講下用p or q 有咩用...對我黎講條數咪又係咁計 個答案純粹係p 用 mu, q 用 r, 同埋有個lambda

有冇人學完Stochastic calculus之後學過Malliavin calculus

Of course, but not sure how to do a pm here

估唔到有人學過，好正

巴打求指教 Malliavin Calculus係講乜嘅?

好難一句講完 但係可以用嚟計Greek 可以對random variable做integration by parts

Let me find a way.

You can think of it as stochastic calculus of variation

This is just another name of Malliavin calculus 咁同冇講過有咩分別

You have to be very careful. It’s not another name of Malliavin calculus, but you can think of it as an analogue. It starts from chaos expansion and mostly deals with things that are Gaussian. I don’t know much about it though.

You're telling someone who learned it that Malliavin calculus is not the same thing as stochastic calculus of variations, which the converse is stated widely in standard monographs of this subject.

You can draw an analogy between Malliavin calculus and calculus of variation. It’s like saying SDE is stochastic version of differential equation. They’re analogies but definitely NOT the same thing.
Again, you have to be very careful about the distinction between analogy and generalisation in mathematics.

Btw are you from HK? I am not aware of anyone in HK is working on Malliavin calculus.

I know it was called stochastic calculus of variation and maybe that’s why it’s confusing.

Actually, a friend of mine was talking about this during dinner awhile ago. That Malliavin calculus concerns Gaussian noise, but by calling it “stochastic” one would assume it works on a wider class of processes, like semimartingales. And we joked about maybe that’s why it’s not called stochastic calculus of variation anymore. He’s doing research on Malliavin calculus and is connected to Malliavin.

So what is you phd in? Are you still doing maths?

maybe opening a new email as a means of chatting will do.