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[問數] Probability theory題目
1. Let `X~N(mu, psi^2)` and `K` be a constant. Calculate
(a) `E(I{X>K})` where `I` is the indicator function.
(b) `E("max"{K-X,0})`.
Hint Use `(K-X) = (K-mu) - (X-mu)`.
(c) `E(e^{tx})`.
Leave answers where appropriate in terms of the normal cumulative distribution function
`Phi(·)`.
2. A random variable `Y` is said to be lognormally distributed with parameters `mu` and `sigma` if
`log Y ~ N(mu, sigma^2)`. We sometimes write `Y ∼"lognormal"(mu, sigma^2)`.
(a) Using your answer to Question 1(c), calculate `E(Y)` and `Var(Y)`.
(b) Suppose `mu = log f - 1/2 sigma^2` for a constant `f>0`.
Calculate `E(Y)` and show that `Var(Y) = f^2 sigma^2` (`1+{sigma^2}/2 + {sigma^4}/6 + `higher order terms).
3. A sequence of random variables `X_0, X_1, ..., X_n, ...` is defined by `X_0 = 1` and `X_n = X_{n-1}xi_{n-1}`, where `xi_i`, `i=0,1,...`, are independent and identically distributed with
\[
\xi_i =
\cases{
1+u & \text{with probability } p\cr
1+d & \text{with probability } 1 – p,
}
\]
where `u>d`.
(a) Calculate `E(X_n|X_{n-1})`.
(b) Let `Y_n = {X_n}/(1+r)^n` for a constant `r>0`.
Find in terms of `p`, `u`, and `d` the value of `r` such that `E(Y_n|Y_{n-1}) = Y_{n-1}`.
Hence find in terms of `u` and `d` the range of such possible values for `r`.
(c) Suppose `E(Y_n|Y_{n-1}) = Y_{n-1}` for all `n`.
Use any result concerning conditional expectation to prove that `E(Y_n|Y_m) = Y_m` for all `n>m>=0`.
4. Show that the first three non-zero terms of the Taylor series for the normal cumulative distribution function `Phi(x)` around zero are
`Phi(x) = 1/2 + x/sqrt{2pi} - {x^3}/{6sqrt{2pi}}`.
Thanks
(a) `E(I{X>K})` where `I` is the indicator function.
(b) `E("max"{K-X,0})`.
Hint Use `(K-X) = (K-mu) - (X-mu)`.
(c) `E(e^{tx})`.
Leave answers where appropriate in terms of the normal cumulative distribution function
`Phi(·)`.
2. A random variable `Y` is said to be lognormally distributed with parameters `mu` and `sigma` if
`log Y ~ N(mu, sigma^2)`. We sometimes write `Y ∼"lognormal"(mu, sigma^2)`.
(a) Using your answer to Question 1(c), calculate `E(Y)` and `Var(Y)`.
(b) Suppose `mu = log f - 1/2 sigma^2` for a constant `f>0`.
Calculate `E(Y)` and show that `Var(Y) = f^2 sigma^2` (`1+{sigma^2}/2 + {sigma^4}/6 + `higher order terms).
3. A sequence of random variables `X_0, X_1, ..., X_n, ...` is defined by `X_0 = 1` and `X_n = X_{n-1}xi_{n-1}`, where `xi_i`, `i=0,1,...`, are independent and identically distributed with
\[
\xi_i =
\cases{
1+u & \text{with probability } p\cr
1+d & \text{with probability } 1 – p,
}
\]
where `u>d`.
(a) Calculate `E(X_n|X_{n-1})`.
(b) Let `Y_n = {X_n}/(1+r)^n` for a constant `r>0`.
Find in terms of `p`, `u`, and `d` the value of `r` such that `E(Y_n|Y_{n-1}) = Y_{n-1}`.
Hence find in terms of `u` and `d` the range of such possible values for `r`.
(c) Suppose `E(Y_n|Y_{n-1}) = Y_{n-1}` for all `n`.
Use any result concerning conditional expectation to prove that `E(Y_n|Y_m) = Y_m` for all `n>m>=0`.
4. Show that the first three non-zero terms of the Taylor series for the normal cumulative distribution function `Phi(x)` around zero are
`Phi(x) = 1/2 + x/sqrt{2pi} - {x^3}/{6sqrt{2pi}}`.
Thanks
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我一看就知這些題目出自 Blyth 那本 Introduction to Quantitative Finance.....
1(a) digital option, (b) put option, (c) mgf
2. lognormal
3. Martingale....
4. saddlepoint approximation
畀你發現到![[sosad]](/face/hkg/sosad.gif)
![[banghead]](/face/hkg/banghead.gif)
究竟呢啲數係咪prob theory入門就會學到？我最近為咗呢幾題(因為想鑽研下QF)，專登走去睇Ross嗰本Introduction to Probability Models，睇咗Expectation嗰個章節都唔識做第一題
相關major的intro就差唔多係呢d
不過呢d係香港的程度係略為難的程度
qf聞說係香港唔係做research其實優勢不大
btw果位巴打連出自邊都知
我純粹係為興趣先想計下QF啲數，睇下可唔可以應用喺market度
好多financial math 書 都要 prob theory / measure theory 底
先睇 david williams, probability with mart
再睇 shreve stochastic calculus for finance i & ii 就perfect 池 la
上面D Statistics題目有2nd year底應該可以KO九成
Undergrad d quant finance多數係旁門左道, skip晒d measure theory 同stochastic analysis
典型例子就係麥當當本derivatives markets, brownian motion個到寫得好含糊
再搭單睇埋
Steele, Stochastic Calculus and Financial Applications
Oksendal, Stochastic differential equations
thx
果然finance都係離唔開stochastic calculus
你可以話 McDonald 本 Derivative Markets 寫得含糊，但 Karlin and Taylor 那套 A First Course in Stochastic Processes / A Second Course in Stochastic Processes 呢? Chapter 15 都係無用measure theory 都講到 Brownian motion, 至於 Ross 那本 Introduction to Probability Models 一樣有 Brownian motion 的 chapter, 係未一樣不需要 measure theory 呢? Lawler 那本 Introduction to Stochastic Processes 又是無提 measure theory ....
或者咁講，我始終覺得唔識同所謂用 Shreve Stochastic Calculus for Finance 所識的只有 epsilon 的分別, 例如 Chung's LIL, Straussen functional LIL 呢? Brownian motion 可以視作 transition semigroup, Markov process, Martingale, 但 finance 那邊除左 Martingale之外好似咩都唔知
另外, rough path 那邊呢? 佢地那邊已經可以用 Generalized Riemann Integration 可以計到 Brownian motion, 甚至更rough的情況.... 當中連一點 measure theory 都不需要, 而又可以直接做 simulation...
所以, 很簡單講先睇 david williams, probability with martingale, 再睇 shreve stochastic calculus for finance i & ii 就perfect, 是太過武斷。
我一看就知這些題目出自 Blyth 那本 Introduction to Quantitative Finance.....
1(a) digital option, (b) put option, (c) mgf
2. lognormal
3. Martingale....
4. saddlepoint approximation
畀你發現到
究竟呢啲數係咪prob theory入門就會學到？我最近為咗呢幾題(因為想鑽研下QF)，專登走去睇Ross嗰本Introduction to Probability Models，睇咗Expectation嗰個章節都唔識做第一題
相關major的intro就差唔多係呢d
不過呢d係香港的程度係略為難的程度
qf聞說係香港唔係做research其實優勢不大
btw果位巴打連出自邊都知
我純粹係為興趣先想計下QF啲數，睇下可唔可以應用喺market度
好多financial math 書 都要 prob theory / measure theory 底
先睇 david williams, probability with mart
再睇 shreve stochastic calculus for finance i & ii 就perfect 池 la
上面D Statistics題目有2nd year底應該可以KO九成
Undergrad d quant finance多數係旁門左道, skip晒d measure theory 同stochastic analysis
典型例子就係麥當當本derivatives markets, brownian motion個到寫得好含糊
再搭單睇埋
Steele, Stochastic Calculus and Financial Applications
Oksendal, Stochastic differential equations
thx
果然finance都係離唔開stochastic calculus
你可以話 McDonald 本 Derivative Markets 寫得含糊，但 Karlin and Taylor 那套 A First Course in Stochastic Processes / A Second Course in Stochastic Processes 呢? Chapter 15 都係無用measure theory 都講到 Brownian motion, 至於 Ross 那本 Introduction to Probability Models 一樣有 Brownian motion 的 chapter, 係未一樣不需要 measure theory 呢? Lawler 那本 Introduction to Stochastic Processes 又是無提 measure theory ....
或者咁講，我始終覺得唔識同所謂用 Shreve Stochastic Calculus for Finance 所識的只有 epsilon 的分別, 例如 Chung's LIL, Straussen functional LIL 呢? Brownian motion 可以視作 transition semigroup, Markov process, Martingale, 但 finance 那邊除左 Martingale之外好似咩都唔知
另外, rough path 那邊呢? 佢地那邊已經可以用 Generalized Riemann Integration 可以計到 Brownian motion, 甚至更rough的情況.... 當中連一點 measure theory 都不需要, 而又可以直接做 simulation...
所以, 很簡單講先睇 david williams, probability with martingale, 再睇 shreve stochastic calculus for finance i & ii 就perfect, 是太過武斷。
Change of measure/Girsanov Theorem都會用到 Radon–Nikodym theorem (a result in measure theory)，有measure theory底的確比較容易理解
Oksendal 本Stochastic differential equations preface 都有講,No previous knowledge about the subject is assumed, but the presentation is based on some background in measure theory.
有錯勿插
Measure theory，之前望過下，苦口良藥來
Measure theory，之前望過下，苦口良藥來
measure theory同functional analysis，用打怪戰形容，算係undergrad數學其中两個好重要既boss
水已潛，bye bye你條尾
Measure theory，之前望過下，苦口良藥來
measure theory同functional analysis，用打怪戰形容，算係undergrad數學其中两個好重要既boss
水已潛，bye bye你條尾
其實我只不過係undergrad stat major students要讀measure theory?
我一看就知這些題目出自 Blyth 那本 Introduction to Quantitative Finance.....
1(a) digital option, (b) put option, (c) mgf
2. lognormal
3. Martingale....
4. saddlepoint approximation
畀你發現到
究竟呢啲數係咪prob theory入門就會學到？我最近為咗呢幾題(因為想鑽研下QF)，專登走去睇Ross嗰本Introduction to Probability Models，睇咗Expectation嗰個章節都唔識做第一題
相關major的intro就差唔多係呢d
不過呢d係香港的程度係略為難的程度
qf聞說係香港唔係做research其實優勢不大
btw果位巴打連出自邊都知
我純粹係為興趣先想計下QF啲數，睇下可唔可以應用喺market度
好多financial math 書 都要 prob theory / measure theory 底
先睇 david williams, probability with mart
再睇 shreve stochastic calculus for finance i & ii 就perfect 池 la
上面D Statistics題目有2nd year底應該可以KO九成
Undergrad d quant finance多數係旁門左道, skip晒d measure theory 同stochastic analysis
典型例子就係麥當當本derivatives markets, brownian motion個到寫得好含糊
再搭單睇埋
Steele, Stochastic Calculus and Financial Applications
Oksendal, Stochastic differential equations
thx
果然finance都係離唔開stochastic calculus
你可以話 McDonald 本 Derivative Markets 寫得含糊，但 Karlin and Taylor 那套 A First Course in Stochastic Processes / A Second Course in Stochastic Processes 呢? Chapter 15 都係無用measure theory 都講到 Brownian motion, 至於 Ross 那本 Introduction to Probability Models 一樣有 Brownian motion 的 chapter, 係未一樣不需要 measure theory 呢? Lawler 那本 Introduction to Stochastic Processes 又是無提 measure theory ....
或者咁講，我始終覺得唔識同所謂用 Shreve Stochastic Calculus for Finance 所識的只有 epsilon 的分別, 例如 Chung's LIL, Straussen functional LIL 呢? Brownian motion 可以視作 transition semigroup, Markov process, Martingale, 但 finance 那邊除左 Martingale之外好似咩都唔知
另外, rough path 那邊呢? 佢地那邊已經可以用 Generalized Riemann Integration 可以計到 Brownian motion, 甚至更rough的情況.... 當中連一點 measure theory 都不需要, 而又可以直接做 simulation...
所以, 很簡單講先睇 david williams, probability with martingale, 再睇 shreve stochastic calculus for finance i & ii 就perfect, 是太過武斷。
Change of measure/Girsanov Theorem都會用到 Radon–Nikodym theorem (a result in measure theory)，有measure theory底的確比較容易理解
Oksendal 本Stochastic differential equations preface 都有講,No previous knowledge about the subject is assumed, but the presentation is based on some background in measure theory.
有錯勿插
我RA見到我書櫃有本williams, 佢話佢睇完之後理解d models 快左好多
巴打講下semi-group對解決咩finance問題有幫助??
有冇巴打可以講下1a，I(X>K)即係乜?
咪Indicator function
我都知係indicator function，但係唔明入面I(X>K)點evaluate
咪Indicator function
我都知係indicator function，但係唔明入面I(X>K)點evaluate
Integration 咯最近失業，我就上下水lah
I（X>K）= 1 when X>K， 0 otherwise
X>K係你成日講既event A， event A 發生， indicator function = 1， 冇發生就等於0
E（I（X>K））= 1 * P（X>K） + 0 * P（X<K） = P（X>K）
I（X>K）= 1 when X>K， 0 otherwise
X>K係你成日講既event A， event A 發生， indicator function = 1， 冇發生就等於0
E（I（X>K））= 1 * P（X>K） + 0 * P（X<K） = P（X>K）
我一看就知這些題目出自 Blyth 那本 Introduction to Quantitative Finance.....
1(a) digital option, (b) put option, (c) mgf
2. lognormal
3. Martingale....
4. saddlepoint approximation
畀你發現到
究竟呢啲數係咪prob theory入門就會學到？我最近為咗呢幾題(因為想鑽研下QF)，專登走去睇Ross嗰本Introduction to Probability Models，睇咗Expectation嗰個章節都唔識做第一題
相關major的intro就差唔多係呢d
不過呢d係香港的程度係略為難的程度
qf聞說係香港唔係做research其實優勢不大
btw果位巴打連出自邊都知
我純粹係為興趣先想計下QF啲數，睇下可唔可以應用喺market度
好多financial math 書 都要 prob theory / measure theory 底
先睇 david williams, probability with mart
再睇 shreve stochastic calculus for finance i & ii 就perfect 池 la
上面D Statistics題目有2nd year底應該可以KO九成
Undergrad d quant finance多數係旁門左道, skip晒d measure theory 同stochastic analysis
典型例子就係麥當當本derivatives markets, brownian motion個到寫得好含糊
再搭單睇埋
Steele, Stochastic Calculus and Financial Applications
Oksendal, Stochastic differential equations
thx
果然finance都係離唔開stochastic calculus
你可以話 McDonald 本 Derivative Markets 寫得含糊，但 Karlin and Taylor 那套 A First Course in Stochastic Processes / A Second Course in Stochastic Processes 呢? Chapter 15 都係無用measure theory 都講到 Brownian motion, 至於 Ross 那本 Introduction to Probability Models 一樣有 Brownian motion 的 chapter, 係未一樣不需要 measure theory 呢? Lawler 那本 Introduction to Stochastic Processes 又是無提 measure theory ....
或者咁講，我始終覺得唔識同所謂用 Shreve Stochastic Calculus for Finance 所識的只有 epsilon 的分別, 例如 Chung's LIL, Straussen functional LIL 呢? Brownian motion 可以視作 transition semigroup, Markov process, Martingale, 但 finance 那邊除左 Martingale之外好似咩都唔知
另外, rough path 那邊呢? 佢地那邊已經可以用 Generalized Riemann Integration 可以計到 Brownian motion, 甚至更rough的情況.... 當中連一點 measure theory 都不需要, 而又可以直接做 simulation...
所以, 很簡單講先睇 david williams, probability with martingale, 再睇 shreve stochastic calculus for finance i & ii 就perfect, 是太過武斷。
Change of measure/Girsanov Theorem都會用到 Radon–Nikodym theorem (a result in measure theory)，有measure theory底的確比較容易理解
Oksendal 本Stochastic differential equations preface 都有講,No previous knowledge about the subject is assumed, but the presentation is based on some background in measure theory.
有錯勿插
我RA見到我書櫃有本williams, 佢話佢睇完之後理解d models 快左好多
巴打講下semi-group對解決咩finance問題有幫助??
唔識
膠登咁多博士撚，我得msc, 之前報過RA都冇人理我, sosad
我一看就知這些題目出自 Blyth 那本 Introduction to Quantitative Finance.....
1(a) digital option, (b) put option, (c) mgf
2. lognormal
3. Martingale....
4. saddlepoint approximation
畀你發現到
究竟呢啲數係咪prob theory入門就會學到？我最近為咗呢幾題(因為想鑽研下QF)，專登走去睇Ross嗰本Introduction to Probability Models，睇咗Expectation嗰個章節都唔識做第一題
相關major的intro就差唔多係呢d
不過呢d係香港的程度係略為難的程度
qf聞說係香港唔係做research其實優勢不大
btw果位巴打連出自邊都知
我純粹係為興趣先想計下QF啲數，睇下可唔可以應用喺market度
好多financial math 書 都要 prob theory / measure theory 底
先睇 david williams, probability with mart
再睇 shreve stochastic calculus for finance i & ii 就perfect 池 la
上面D Statistics題目有2nd year底應該可以KO九成
Undergrad d quant finance多數係旁門左道, skip晒d measure theory 同stochastic analysis
典型例子就係麥當當本derivatives markets, brownian motion個到寫得好含糊
再搭單睇埋
Steele, Stochastic Calculus and Financial Applications
Oksendal, Stochastic differential equations
thx
果然finance都係離唔開stochastic calculus
你可以話 McDonald 本 Derivative Markets 寫得含糊，但 Karlin and Taylor 那套 A First Course in Stochastic Processes / A Second Course in Stochastic Processes 呢? Chapter 15 都係無用measure theory 都講到 Brownian motion, 至於 Ross 那本 Introduction to Probability Models 一樣有 Brownian motion 的 chapter, 係未一樣不需要 measure theory 呢? Lawler 那本 Introduction to Stochastic Processes 又是無提 measure theory ....
或者咁講，我始終覺得唔識同所謂用 Shreve Stochastic Calculus for Finance 所識的只有 epsilon 的分別, 例如 Chung's LIL, Straussen functional LIL 呢? Brownian motion 可以視作 transition semigroup, Markov process, Martingale, 但 finance 那邊除左 Martingale之外好似咩都唔知
另外, rough path 那邊呢? 佢地那邊已經可以用 Generalized Riemann Integration 可以計到 Brownian motion, 甚至更rough的情況.... 當中連一點 measure theory 都不需要, 而又可以直接做 simulation...
所以, 很簡單講先睇 david williams, probability with martingale, 再睇 shreve stochastic calculus for finance i & ii 就perfect, 是太過武斷。
Change of measure/Girsanov Theorem都會用到 Radon–Nikodym theorem (a result in measure theory)，有measure theory底的確比較容易理解
Oksendal 本Stochastic differential equations preface 都有講,No previous knowledge about the subject is assumed, but the presentation is based on some background in measure theory.
有錯勿插
我RA見到我書櫃有本williams, 佢話佢睇完之後理解d models 快左好多
巴打講下semi-group對解決咩finance問題有幫助??
唔識
膠登咁多博士撚，我得msc, 之前報過RA都冇人理我, sosad
報咩RA?
我一看就知這些題目出自 Blyth 那本 Introduction to Quantitative Finance.....
1(a) digital option, (b) put option, (c) mgf
2. lognormal
3. Martingale....
4. saddlepoint approximation
畀你發現到
究竟呢啲數係咪prob theory入門就會學到？我最近為咗呢幾題(因為想鑽研下QF)，專登走去睇Ross嗰本Introduction to Probability Models，睇咗Expectation嗰個章節都唔識做第一題
相關major的intro就差唔多係呢d
不過呢d係香港的程度係略為難的程度
qf聞說係香港唔係做research其實優勢不大
btw果位巴打連出自邊都知
我純粹係為興趣先想計下QF啲數，睇下可唔可以應用喺market度
好多financial math 書 都要 prob theory / measure theory 底
先睇 david williams, probability with mart
再睇 shreve stochastic calculus for finance i & ii 就perfect 池 la
上面D Statistics題目有2nd year底應該可以KO九成
Undergrad d quant finance多數係旁門左道, skip晒d measure theory 同stochastic analysis
典型例子就係麥當當本derivatives markets, brownian motion個到寫得好含糊
再搭單睇埋
Steele, Stochastic Calculus and Financial Applications
Oksendal, Stochastic differential equations
thx
果然finance都係離唔開stochastic calculus
你可以話 McDonald 本 Derivative Markets 寫得含糊，但 Karlin and Taylor 那套 A First Course in Stochastic Processes / A Second Course in Stochastic Processes 呢? Chapter 15 都係無用measure theory 都講到 Brownian motion, 至於 Ross 那本 Introduction to Probability Models 一樣有 Brownian motion 的 chapter, 係未一樣不需要 measure theory 呢? Lawler 那本 Introduction to Stochastic Processes 又是無提 measure theory ....
或者咁講，我始終覺得唔識同所謂用 Shreve Stochastic Calculus for Finance 所識的只有 epsilon 的分別, 例如 Chung's LIL, Straussen functional LIL 呢? Brownian motion 可以視作 transition semigroup, Markov process, Martingale, 但 finance 那邊除左 Martingale之外好似咩都唔知
另外, rough path 那邊呢? 佢地那邊已經可以用 Generalized Riemann Integration 可以計到 Brownian motion, 甚至更rough的情況.... 當中連一點 measure theory 都不需要, 而又可以直接做 simulation...
所以, 很簡單講先睇 david williams, probability with martingale, 再睇 shreve stochastic calculus for finance i & ii 就perfect, 是太過武斷。
Change of measure/Girsanov Theorem都會用到 Radon–Nikodym theorem (a result in measure theory)，有measure theory底的確比較容易理解
Oksendal 本Stochastic differential equations preface 都有講,No previous knowledge about the subject is assumed, but the presentation is based on some background in measure theory.
有錯勿插
我RA見到我書櫃有本williams, 佢話佢睇完之後理解d models 快左好多
巴打講下semi-group對解決咩finance問題有幫助??
唔識
膠登咁多博士撚，我得msc, 之前報過RA都冇人理我, sosad
報咩RA?
UST math department 一個做financial math ， derivatives pricing 既research assistant
最近失業，我就上下水lah
I（X>K）= 1 when X>K， 0 otherwise
X>K係你成日講既event A， event A 發生， indicator function = 1， 冇發生就等於0
E（I（X>K））= 1 * P（X>K） + 0 * P（X<K） = P（X>K）
屌，原來真係咁
我一看就知這些題目出自 Blyth 那本 Introduction to Quantitative Finance.....
1(a) digital option, (b) put option, (c) mgf
2. lognormal
3. Martingale....
4. saddlepoint approximation
畀你發現到
究竟呢啲數係咪prob theory入門就會學到？我最近為咗呢幾題(因為想鑽研下QF)，專登走去睇Ross嗰本Introduction to Probability Models，睇咗Expectation嗰個章節都唔識做第一題
相關major的intro就差唔多係呢d
不過呢d係香港的程度係略為難的程度
qf聞說係香港唔係做research其實優勢不大
btw果位巴打連出自邊都知
我純粹係為興趣先想計下QF啲數，睇下可唔可以應用喺market度
好多financial math 書 都要 prob theory / measure theory 底
先睇 david williams, probability with mart
再睇 shreve stochastic calculus for finance i & ii 就perfect 池 la
上面D Statistics題目有2nd year底應該可以KO九成
Undergrad d quant finance多數係旁門左道, skip晒d measure theory 同stochastic analysis
典型例子就係麥當當本derivatives markets, brownian motion個到寫得好含糊
再搭單睇埋
Steele, Stochastic Calculus and Financial Applications
Oksendal, Stochastic differential equations
thx
果然finance都係離唔開stochastic calculus
你可以話 McDonald 本 Derivative Markets 寫得含糊，但 Karlin and Taylor 那套 A First Course in Stochastic Processes / A Second Course in Stochastic Processes 呢? Chapter 15 都係無用measure theory 都講到 Brownian motion, 至於 Ross 那本 Introduction to Probability Models 一樣有 Brownian motion 的 chapter, 係未一樣不需要 measure theory 呢? Lawler 那本 Introduction to Stochastic Processes 又是無提 measure theory ....
或者咁講，我始終覺得唔識同所謂用 Shreve Stochastic Calculus for Finance 所識的只有 epsilon 的分別, 例如 Chung's LIL, Straussen functional LIL 呢? Brownian motion 可以視作 transition semigroup, Markov process, Martingale, 但 finance 那邊除左 Martingale之外好似咩都唔知
另外, rough path 那邊呢? 佢地那邊已經可以用 Generalized Riemann Integration 可以計到 Brownian motion, 甚至更rough的情況.... 當中連一點 measure theory 都不需要, 而又可以直接做 simulation...
所以, 很簡單講先睇 david williams, probability with martingale, 再睇 shreve stochastic calculus for finance i & ii 就perfect, 是太過武斷。
Change of measure/Girsanov Theorem都會用到 Radon–Nikodym theorem (a result in measure theory)，有measure theory底的確比較容易理解
Oksendal 本Stochastic differential equations preface 都有講,No previous knowledge about the subject is assumed, but the presentation is based on some background in measure theory.
有錯勿插
我RA見到我書櫃有本williams, 佢話佢睇完之後理解d models 快左好多
巴打講下semi-group對解決咩finance問題有幫助??
唔識
膠登咁多博士撚，我得msc, 之前報過RA都冇人理我, sosad
有master都好撚勁啦
唔識
膠登咁多博士撚，我得msc, 之前報過RA都冇人理我, sosad
報咩RA?
UST math department 一個做financial math ， derivatives pricing 既research assistant
你現職做緊乜?
唔識
膠登咁多博士撚，我得msc, 之前報過RA都冇人理我, sosad
報咩RA?
UST math department 一個做financial math ， derivatives pricing 既research assistant
你現職做緊乜?
都同計數有關，完左，冇續約
即係係屋企hea ?
世事都被你看透
學左乜野叫stochastic
random walk
再少少basic option既野 put call etc先好繼續落去啦
random walk
再少少basic option既野 put call etc先好繼續落去啦
學左乜野叫stochastic
random walk
再少少basic option既野 put call etc先好繼續落去啦
利申math and finance
搭單之後睇partial d eq
之後望下black-scholes model同 binomial model
之後望下black-scholes model同 binomial model
搭單之後睇partial d eq
之後望下black-scholes model同 binomial model
啲人話black-scholes formula只係toy
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