Introduction to Stochastic Calculus & Application in Finance

btw我呢兩三日都應該出唔到post
幾個midterm打到埋身 想抽時間都抽唔到

完咗midterm之後我應該會整一個review先
同大家複習返我地依家嘅進度

同埋會補充返一啲basic嘅嘢
例如pdf,cdf,mean,var 呢啲基礎嘅stat knowledge

仲有會講下一啲basic嘅derivative product同concept
e.g. (future, call, put, barrier options, European/American style, exotic options,bond之類)
等冇乜fina底嘅觀眾都可以理解我之後做緊乜

完咗個review就會入下一個section —— Black Scholes Merton Model

我n展都要讀ODE同少少PDE,stat反而冇學會唔會太過份

lm

樓主可唔可以講下點樣由零數底學到呢一步？

Ito lemma
要由最fundamental ge calculus definition入手

Math
-中學數
-m2 (basic calculus & linear algebra)
-a level pure math
-university math (formal calculus and more related theorems)
-Linear algebra
-Multi-variable calculus (d同in)
-ODE+PDE

Stat
-Basic concept (mean,var,cov,corr,pdf,cdf,joint dist, conditional prob/dist)
-Overview of different distributions (binomial,poison,geometric,negative binomial,uniform,normal,exponential,gamma,beta,student t,F,χ^2)
-Useful theorems (CLT/FCLT, Law of large number)
-Hypothesis testing
-Regression
-Statistical Inference
-Time series

我當初大概就係咁樣學上去 (不過我未take PDE)
當然仲有其他嘢係可以讀

e.g. real analysis
因為probability thoery其實就係由real analysis整出黎(確切啲講係measure theory)
讀埋呢個你睇任何stat同mathematical finance嘅proof都唔會有問題
p.s. 如果你唔係勇者就唔好讀啦
———————
其實就咁讀finance的確係唔需要學咁多數
9成都係作文老吹睇表畫線
就算真係學都應該學programming

但係如果你學嘅係risk man
咁數底就好重要 因為我地好多時都需要依靠model黎approximate一啲”risk”
而呢啲model就係用上面嘅數去build up
始終risk呢樣嘢冇得靠吹水作文

welcome to real analysis

stat方面有乜參考書

我讀過嘅stat course多數都係下面呢幾本

Hogg, R. V. , Tanis, E. A. Zimmerman, D. L. (2015) Probability and Statistical Inference, 9th edition, Pearson.

Suhov, Y. and Kelbert, M. (2005) Probability and Statistics by Example: Volume
1, Basic Probability and Statistics. Cambridge, UK; New York: Cambridge University Press.

Hogg, McKean and Craig (2005) Introduction to Mathematical Statistics, 6th
edition, Prentice Hall.

Casella, G. and Berger, R. L. (2002). Statistical Inference, Duxbury Press.

thanks, 我想問啲書exercise會做幾多，揀邊啲嚟做？

Strong post li, btw 無讀過a math 有無得救

我其實都冇乜做過ref book嘅exercise 所以呢個真係答唔到你
通常我都係lecture/tutorial notes睇唔明先會睇埋ref book

不過我諗都冇需要做曬 (每題都做實在太曬時間)
做exercise到頭黎其實都係想確保自己concept冇錯
真係難同抽象嘅section就睇多幾條

支持樓主 呢個Course係某stat related major號稱最難,樓主應該幫到唔少人
可惜我上個SEM讀左, 我地相逢恨晚

冇話有冇得救嘅 都係睇你肯花幾多時間去學

如果要學到睇得明stoc cal 我覺得下面呢啲野係最重要

-Linear algebra
因為high dimensional嘅野通常都係用matrix同vector form寫低
同埋對之後simulation都有用

-Multi-variable calculus (d同in)
呢個唔洗講點解有用啦

-ODE+PDE
你見ito's lemma個樣同pde咁似 就知道學埋ode pde實無死
同埋之後講到black scholes你就會見到pde同stoc cal其實好有關係

-Basic stat (moment, distribution, CLT/FCLT, law of large number)
始終應用得最多stoc cal嘅field就係finance
而finance關心嘅野其實好多時都係一啲stat嘅問題 (Mean = average, std dev = volatility 之類)
所以係需要一啲stat嘅background

-Stochastic process
雖然我只係講咗wiener process 但係其實仲有好多其他嘅random processes
(e.g. Bernoulli process, poisson process)
而本身random process已經有好多野可以講
(e.g. markov chain, transition prob matrix, birth death process)
而stoc cal其實就係建基於呢啲野 再去問啲類似"rate of change"嘅問題

留名

lm

以前學過，但最後一堂阿 sir 先同我地講 derivatives quant 已經收左皮，叫我地向第二個方向發展

細電仔留名
玩signal processing
一堆stat野

幾時講到equivalent martingale measure

就快
講到Feynman Kac其實就係risk neutral measure

DSP 仲難過 quant fin, 我覺得。

點樣收皮法
我都係做呢行 都仲係好需要人才