h**********c
发帖数: 4120 | 1 天津张大民的 stochastic transformation of verbal space 怎么样? |
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x*******7
发帖数: 409 | 2 Fundamentals of Probability, with Stochastic Processes (3rd Edition)
电子版,最好有中文译本:)免费下载也可以,谢谢 |
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d********n
发帖数: 34 | 3 请问谁有Ikeda的Stochastic Differential Equations and Diffusion Processes吗？
这本书out of print了，图书馆的又很抢手。谢啦~ |
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n******t
发帖数: 189 | 4 【 以下文字转载自 Quant 讨论区 】
发信人: niuzhist (niuzhist), 信区: Quant
标 题: Stochastic Differential Equations
发信站: BBS 未名空间站 (Sun Apr 17 13:54:24 2011, 美东)
which department usually has this kind of course? Math?
I can not find the related one in any department of my university... |
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w*******e
发帖数: 902 | 5 这个一般都是数学系吧
【 以下文字转载自 Quant 讨论区 】
发信人: niuzhist (niuzhist), 信区: Quant
标 题: Stochastic Differential Equations
发信站: BBS 未名空间站 (Sun Apr 17 13:54:24 2011, 美东)
which department usually has this kind of course? Math?
I can not find the related one in any department of my university... |
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n**h
发帖数: 22 | 6 请问对于stochastic process有没有类似slutsky的theorem？比如：X_n(t) weakly
converges到一个tight的G(t) process，同时Y_n(t) uniformly converges到一个
deterministic的process H(t)，那么可不可以推出X_n(t)*Y_n(t) converges到G(t)*H
(t)？
多谢！ |
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Q***5
发帖数: 994 | 7 tau 是什么？如果是常数，而且f 不病态的话，应该没问题。其实这个算不上是
stochastic integration。 |
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c**a
发帖数: 316 | 8 Please help!
X(t) is the stochastic exponential of a standard Brownian motion,
i.e. X(t) = exp(w(t) - 0.5 t), w(t) being a standard Brownian motion.
What is the probability that X(T) is greater than H (>1)?
My solution:
log(X(T)) > log (H)
=>
w(T) - 0.5 T > log(H)
=>
w(T) > log(H) + 0.5 T
=>
y > log(H)/sqrt(T) + 0.5*sqrt(T) where y is a standard normal r.v.
The PROBLEM is as T approaches +inf
[log(H)/sqrt(T) + 0.5*sqrt(T)] approaches +inf as well.
Hence, we have y > +inf.
Hence, the probability ... 阅读全帖 |
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B*********h
发帖数: 800 | 9 ☆─────────────────────────────────────☆
cedar23 (Cedar) 于 (Thu Apr 5 11:06:16 2007) 提到:
for pricing a vanilla option, which one will get a higher value, local vol
or stochastic vol?
☆─────────────────────────────────────☆
wusuowei (student) 于 (Thu Apr 5 11:17:55 2007) 提到:
where did you get the question?
☆─────────────────────────────────────☆
zouzou (zouzou) 于 (Thu Apr 5 20:29:02 2007) 提到:
why use a model? Just read from the market.
☆─────────────────────────────────────☆
t |
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Q***5
发帖数: 994 | 11
(1) By definition of BM, E((B(t)-B(s))^2) = t-s (assume t>s)
So E(B(t)^2)-2E(B(t)B(s))+E(B(s)^2) = t-s, and we know E(B(s)^2) =s, hence
the result: E(B(t)B(s)) = s
(2) I guess this one use some kind of change of oder of integeration:
\int_0^T B_t dt = \int_0^T \int_0^t d(B_s) dt = \int_0^T\int_s^T dt dB_s = \
int_0^T (T-s)dB_s
The variance of this random variable is \int_0^T (T-s)^2ds
Can some experts shed light on the condition of changing order of
integeration in stochastic calculus? |
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d*******n
发帖数: 524 | 12 谁有这个paper：
E. Platen,
An introduction to numerical methods for stochastic differential equations
Acta Numer., 8(1999), 197-246
可不可以给我发一份？
谢谢了 |
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B*******t
发帖数: 135 | 13 不好意思，不是我偷懒，做了好半天的，实在是才疏学浅没做出来。
据说这里牛人多，啥题目都能解决，所以来这里请教一下。
Steele 书(Stochastic Calculus and Financial Applications, J. Michael Steele)
上的 7.2 & 7.3
7.2
Show that if X_t is any continuous martingale and \phi is any convex
function, then Y_t=\phi(X_t) is always a local submartingale. Give an
example that shows Y_t need not be an honest submartingale.
7.3
Show that if X_t is a continuous local submartingale such that
E(sup_{0<=s<=T} |X_s|) < inf,
then {X_t:0<=t<=T} is an honest submartingale. Show h |
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m******c
发帖数: 55 | 14 本人CS背景，这学期学习Stochastic Calculus这门课, 有很多问题不是很明白。
哪位同学有兴趣当一下tutor, 请联系r******[email protected]
时间，报酬面议。 |
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c*******e
发帖数: 150 | 15 note that the process Y_t satisfies dY_t = T_t Y_t dW_t
it is called the stochastic exponential of (T_t)_{t\in[0,T]}, sometimes
denoted as \epsilon(T)_t
If (T_t)_{t\in[0,T]} satisfies the Novikov condition, i.e.
\mathbb{E}[exp(1/2 \int_0^T T_s^2 ds)] < +\infty
then Y_t is also called an exponential martingale, since it is a true
martingale on [0, T] |
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z**k
发帖数: 378 | 17 面了三个基本的stochastic calculus积分，答出来前两个，最后一个弃了： assume B_t is
the standard brownian
motion:
1) \int_0^T t dB_t. This I know the solution is Normal with mean 0 and
variance t^2
2) \int_0^T B_t dB_t. The solution is .5B_t^2 - .5T^2
3) \int_0^T B_t dt. ：( 这个我就不会了。。。算了好久还是放弃了
我尝试用finite sum and take limit来解，面试官似乎希望我能直接报答案。。。不
得已放弃
了。 |
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d********n
发帖数: 34 | 18 请问谁有Ikeda的Stochastic Differential Equations and Diffusion Processes吗？
这本书out of print了，emule上没找到，图书馆的又很抢手。谢啦~ |
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w********r
发帖数: 9 | 19 Does non-stochastic mean predictable? Not necessary to be constant? |
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w********r
发帖数: 9 | 20 like non-stochastic interest rate? |
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c**********e
发帖数: 2007 | 21 X_t is a stochastic process which satifies
d X_t = X_t^{1.5} dB_t?
What is the distribution of X_t? |
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a********e
发帖数: 78 | 22 请推荐 用Ｒ模拟 stochastic process的书或讲义，website? 感谢。 |
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n*******e
发帖数: 107 | 23 我又model啊，一个price符合某个stochastic process
这个process有三道四个未定参数，但是形式确定
就要由history来fit那四个参数 |
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w**********y
发帖数: 1691 | 24 这么说不太对.一条path是可以fit参数的,time series里面的AR,ARMA都是一条path去
fit.OU process当然也是.
以前有一些用MCMC(Bayes)的方法去fit,这个方法几乎是万能的,可以fit各种复杂的
stochastic volatility model,但是时间性和可靠性可能会很不好..
Chicago的Nicholas Polson有这方面的paper
应该kalman filter啊,particle filter啊也能做..
对于一般的diffusion,很多人都做过相关research,参看:
Maximum-Likelihood Estimation of Discretely-Sampled Diffusions: A Closed-
Form Approximation Approach, Econometrica, 2002, 70, 223-262
Yacine Sahalia的主页上有matlab的code. 他还有其它几篇关于model fitting的paper.
对于如何根据Derivative的价格去calibra... 阅读全帖 |
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B*********h
发帖数: 800 | 25 那就说说吧。以我愚见，calibration的目的不是预测，而是寻求一致性。回到最简单
的问题，你问什么要调参数？因为你希望你的模型能够和数据一致，或者是和产生数据
的原始process一致。这个就是LZ所追求的,但是实际是达不到的，所以要把这个fit的
概念弱化。
比如说你有一个简单的GBM模型，你要给一个OTC产品定价，首先你要确定的就是如果用
这个模型给最简单的listed vanilla option定价，是否和市场价一致？如果连这个都
达不到，显然得出的更复杂的产品定价和市场也不一致。
这个时候你就开始tweak模型。然后发现你的模型定价和市场不一致的原因，比如说
vanilla option, OTM put/call和ATM的implied volatility不同。这个和GBM的
constant volatility假设相悖。然后你就开始堆process,加参数。就算上了
stochastic volatility,发现还是不能和市场一致。然后直觉上因为股价是有jump的，
所以你在模型里加上这个。最后这样你发现你的模型里不同的feature足够多了（也就
是参数足够... 阅读全帖 |
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z****u
发帖数: 185 | 26 Sigh, isn't it disappointing ? These stochastic vol jumping bullshit,
pacifying pills, far away from helping make money or manage risk.
When market tumbled in 2008, many exotic equity trading desks featuring all
kinds of fancy models were screwed. The larger the business, the worse.
All models are wrong. |
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a*********r
发帖数: 139 | 27 First, SDE is another way to state the Ito integral. Since the integrand is
not stochastic, the integral is actually a one-dimensional Wiener integral.
The variance is readily computed from the well-known formula. |
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w******i
发帖数: 503 | 28 perfect background, stochastics + c++, for a research quant.. |
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w******i
发帖数: 503 | 29 perfect background, stochastics + c++, for a research quant.. |
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s*****g
发帖数: 77 | 30 请问版上的大牛们，这两个哪个更好一点？为什么？
我觉得implied vol假设是constant，所以用起来更简单直观。但是stochastic vol的
话更接近事实，因为vol不可能是常数啊。所以这两个哪个更好，各自有什么用处啊？ |
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x******l
发帖数: 104 | 31 Can anyone advice me some books?
I need Algorithms and programs (in Matlab, VB, VC++) for stochastic calculus
, multivariate calculus, linear algebra, differential equations, probability
theory and statistical inference.
I need some good books or resouces to understand how to program for finance. |
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r**a
发帖数: 536 | 32 金融里面啥样的工作岗位会用到stochastic optimal control？这里排除掉american
option那种optimal stopping theory. |
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r**a
发帖数: 536 | 33 金融里面啥样的工作岗位会用到stochastic optimal control？这里排除掉american
option那种optimal stopping theory. |
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m*********g
发帖数: 646 | 34 i don't quite understand, are you looking for an intern position which
mainly research stochastic calculus? I think a post-doc main be the ideal
choice for that...
I think companies like ITG may fit you better. |
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A*****s
发帖数: 13748 | 35 比如去年看到一个Constellation Energy的intern
需要懂stochastic calculus，需要FDM之类的
当时忙，没法申
现在想集中找类似的position，哪里找？谢谢！ |
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x******a
发帖数: 6336 | 36 I did on indeed.com
it seems that many positions which require stochastic calculus would require
3+ years working experience as well. |
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w******n
发帖数: 645 | 37 I'm sorry, I thought it too quickly.
The actual reason is that we cannot think dB*dB=dt as it's mean. It's simply
a statement that Brownian motion accumulates quadratic variation at rate
one per unit time. It's just an informal writing and it's only meaningful
when you do integral.
In Shreve's book, section 3.4, we get the below explanations.
Assume approximation dB ~ B(t_i+1)-B(t_i), for a partition 0= t_0 < t_1 <...
....
Now we have E[(B(t_i+1)-B_(t_i))^2] = t_i+1-t_i ~dt, Var[(B(t_i+1)... 阅读全帖 |
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L*******t
发帖数: 2385 | 38 random measure，你是在看jump吧？那部分本身就比较难理解的。
我觉得你可以分两步走，先看看实分析，再研究Stochastic process。
没有real analysis的基础，搞SP会觉得很困难，处处受限制。
functional analysis的banach space最好也看看。
GOOGLE上讲义很多，建议看讲义，篇幅不长，高度概括。
每天看个10页，10-20天就能看完所有的东西了应该 |
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s******e
发帖数: 1751 | 39 have you backtested holding an 105% OTM SPX call? I don't see anything wrong
w/ just using BS vol. In another word, i don't see any needs to invent some
fancy model for an deep OTM european option.
before you spend so much time reading those published stuff, what problem
you try to solve? Recall why heston invented stochastic vol? what problem
he was trying to solve? |
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L*******t
发帖数: 2385 | 40 glad to see so many experts here!
很多academic paper都似乎只是在讨论价格，虽然也有许多直接讨论hedging的。但我
的重点似乎都放在了前者，业界似乎更加在乎hedging吧。因为价格总有办法得到。而
hedging看上去tricky一些。。
在option market，应该有arbitrage的机会吧？或者因为流动性，没人去地上捡这些小
钱？
我的感觉是no arbitrage-> posotive sdf-> change of mmeasure这套东西很难
reconcile
market data了，local stochastic vol这套工具只能对path independent的产品定价
，似乎也走不通了。我曾经向我老板建议不通的产品似乎隐含不同的sdf，因为人们交
易不同产品的时候对future的views是不一样的，被无情的批了一顿。
对option pricing和hedging，你有什么建议么？
be |
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h*****g
发帖数: 944 | 41 本人做time series, stochastic optimization 研究的，不知道哪些知识可以用在
quant上。
正在写简历，想突出一下目前研究上，能用到financial market 上的东西 |
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A*******s
发帖数: 3942 | 42 Wondering if there is any easy-to-implemented algorithm to get the i-th
stochastic root of a transition matrix. Any reference? |
|
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A*******s
发帖数: 3942 | 44 root matrix that has the stochastic (transition) matrix property (row sum=1
and non negative real elements) |
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A*******s
发帖数: 3942 | 45 thanks a lot. but i don't think this solution guarantees a stochastic root,
but ur reference is helpful. |
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L*******t
发帖数: 2385 | 46 居然还发到大数学版去了，
以后有stochastic的问题来我们大金工版问。 |
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j******n
发帖数: 91 | 47 两个call. 一个constant volatility 40%, 一个stochastic volatility with mean
40%. 问两个哪个值钱。
option price is in most cases a convex function of volatility. 所以是由
convex property, constant volatility 的那个option 更值钱。对吗？ |
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B*******t
发帖数: 135 | 48 不好意思，不是我偷懒，做了好半天的，实在是才疏学浅没做出来。
刚刚看到置顶，所以声明一下，跟面试没关系，就是作业题。
Steele 书(Stochastic Calculus and Financial Applications, J. Michael Steele)
上的 7.2 & 7.3
7.2
Show that if X_t is any continuous martingale and \phi is any convext
function, then Y_t=\phi(X_t) is always a local submartingale. Give an
example that shows Y_t need not be an honest submartingale.
7.3
Show that if X_t is a continuous local submartingale such that
E(sup_{0<=s<=T} |X_s|) < inf,
then {X_t:0<=t<=T} is an honest submartingale. Show |
|
y******e
发帖数: 133 | 49 最近要转一门课stochastic processes的课程。因为是在国内上的，所以要翻译一下。
小弟不是STAT，也不是数学。所以请人帮忙看看自己翻译的对不对？谢谢了 |
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h******a
发帖数: 198 | 50 Karlin A first course in Stochastic Process |
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