Q***5
发帖数: 994 | 1 I'm reading Oksendal's Stochastic Differential Equation,
http://books.google.com/books?id=kXw9hB4EEpUC&lpg=PP1&dq=oksend
Theorem 8.4.3, it seems that in the proof of sufficiency, only E^x(v v^t| N_
t) = \sigma \sigma^T(Y_t^x) is needed. This means that, all other conditions
hold,
E^x(v v^t| N_t) = \sigma \sigma^T(Y_t^x) implies that
v v^t( t,w) = \sigma \sigma^T(Y_t^x (w)), a little bit surprising, isn't it?
Can some experts of Stochastic process confirm?
Thanks |
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l*******z
发帖数: 108 | 2 多谢解答。
应该\rho >\mu
我总结了下，这类问题应该这样解：
1.判断是第一次达到x*的时候就应该stop，用到oksendal-Stochastic differential equations 第十章的内容。
2.之后就是解一个PDE，这里的期望里是积分，相当于是Possion 问题。在 oksendal-Stochastic differential equations 第9章里有讲。
此类的问题就是解 Av+f=0
这里是
Vt+mu*x*Vx+0.5 sig^2 x^2 Vxx+f=0
Vx represent the derivative of V respect to x.
边界条件怎么弄？
3.解出v(s,x)的表达式后，把v当成x的函数，求极值，就可以解出x*。
4.如果没有积分就直接是Av=0,对应于 Dirichlet 问题，如果都有
v=E[integral(f(x))+ g(x)],就应该是Dirichlet-Possion混合问题。
不知道以上是否有错，望指正！
Springer |
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H****h
发帖数: 1037 | 3 世界图书出版公司出版的英文书
Stochastic Differential Equations
Bernt Oksendal
看看是否能适合你。
另外好象没有基于泊松过程的推导。
一般都是从布朗运动Brownian motion
或连续鞅continuous martingale出发。 |
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f******k
发帖数: 297 | 4 check out Oksendal's book, it is pretty easy to begin with.
or if you want to avoid discussion of predictive process,
check out Protter's book.
for Poisson process, if you are talking about Poisson process
driven SDE, then almost all books include this, since most of
books based on martingale to define stochastic calculus, and it's
just natural extention to include process with jumps like Poisson
process. |
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k*******l
发帖数: 69 | 5 don't know what you want to get
the RN derivative of which measure wrt which measure???
possibly u could look at Oksendal's Applied Stochastic Control of Jump
Diffusions, Ch. 1
and
we |
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e***x
发帖数: 13 | 6 why don't you just search amazon, if popularity is all your concern. The top
one, I guess, is Oksendal's. For beginner, I think Evan's is better. You
may find a copy by google. |
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k*******l
发帖数: 69 | 7 i guess the quote by Oksendal is not from himself (at least the last
sentence)
seems to be from somebody else
懂他
记录
能停
行空
相信
have
higher |
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d***q
发帖数: 1119 | 9 stochastic differential equations by oksendal 不错。
introduction to stochastic differential equations by thomas C. Gard
也不错 。。这本现在没有新货卖得了，比较可惜.. |
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s*****u
发帖数: 164 | 10 可以考虑先看一下 Shreve 的 Stochastic Calculus for Finance, Vol II 的前六章，
这本书写的比较直观。然后可以看看 Oksendal 的 Stochastic Differential
Equation。 |
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f**********d
发帖数: 4960 | 11 thx, Oksendal这本似乎是很经典的，很多人推荐。
章， |
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a**********n
发帖数: 5 | 12 [1] Stochastic Differential Equations: An Introduction with Applications
by B K Ksendal, Bernt Oksendal
比较容易入门，需要probability的知识。
[2] Continuous Martingales and Brownian Motion by Daniel Revuz and Marc Yor
1999
经典教材,难度较大，适合长期反复阅读,简洁严谨。
[3] Stochastic Integration and Differential Equations by Philip Protter
从Levy Process 的观点入手，风格清爽，发人深思， 难度较大。Levy Process 正成为
随即分析，数学金融的研究热点，因为Brownian Motion考虑的是连续的随机过程，而
Levy Process是带有Jump的process。 当然Brownian motion 就是Levy Process 的特殊
例子。
[4] Brownian Motion and |
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r*****t
发帖数: 286 | 13 ☆─────────────────────────────────────☆
liangstone (stone) 于 (Sat Mar 24 06:35:40 2007) 提到:
大家觉得那些书比较好啊？
按照低，中，高级给评评？
STEVEN E SHREVE 的 stochastic calculus for finance II 怎么样？难度等级属于哪
个呀
相比较其它比较热门的书有什么优缺点啊？
谢谢
☆─────────────────────────────────────☆
litaihei (李太黑) 于 (Sat Mar 24 11:48:28 2007) 提到:
如果理科背景很强，STEVEN E SHREVE 的书很值得一看。特别是前六章的一些概念。网
上有本免费的STEVEN E SHREVE 的书，写的太简略，看起来不爽。stochastic
calculus for finance II 概念写的很清楚。 Oksendal 的书也不错，我觉着没必要全
看懂，作作书里的习题会很有帮助。
☆─────────────────────── |
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t********t
发帖数: 1264 | 14 good book but pretty hard, mostly about stochastic analysis. it's an
overkill for regular math finance stuff.
by level of difficulties
Protter > Karatzas&Shreve >> Oksendal |
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P*********t
发帖数: 4451 | 15 You are talking about Oksendal's book.
LZ is asking for a book that is out of print. Hard to imagine something went
through at least 6 editions AND went out of print... |
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b***k
发帖数: 2673 | 16 55555555
ms是我isometry理解不够，可是我看到的都是带平方的情况，
你这个式子好像更加general的情况，
请问有reference吗？
我在Oksendal的书上没有看到啊。 |
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f****u
发帖数: 50 | 17 也有犹豫要不要把这个发上来，最后还是贴上来了，望水车轻拍，高人不吝赐教。
背景：清华本科，美国二类重点大学偏重计算和物理的工学博士，数学和统计较好，编
程一般，无实际金融工作经验。
摘要：陆续准备quant有两年，至今电话面试5次，全部fail，求高人指点迷津。
准备情况：
-重点围绕面试四大名著，几乎所有题都做了一遍，有些重点部分看了两到三遍。
-学习了Stochastic Calculus的两到三本经典书籍 (Oksendal + Shreve + Michael
Steel)
-学了Derivative Pricing的几本书(John Hull + Mark Joshi)
-C++ 编程方面 (Primer + Mark Joshi + Some interview questions prepared)
面试情况：
MS: 过了HR的两轮电话面试，几乎全是brainteaser，第三轮碰到一个学计算数学的中
国人，英语还没有我好，交流有问题，来回几个问题之后结束。感觉不好，后来告知
fail了。
GS: 面了两个组。第一个是equity quant research组，是个很... 阅读全帖 |
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k***t
发帖数: 57 | 18 不知这个单子的面向对象是什么
大概看了看 似乎列了40来本 不知道看到哪个程度可以应付quan的面试 又或后面的
hardcore是工作后的进阶的
本人fresh phd还没毕业 大概还有一年多的时间 理工背景 统计有时用用 不知道如何
利用这个书单
谁能指点一下吧 谢了先
////////////////////////////////////////////////////////////////////////////
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///////////////////
0.0 First steps -- General:
A. Black Scholes and Beyond: Option Pricing Models, N A Chriss
B. Derivative Securities, R Jarrow, S Turnbull
C. Introduction to Mathematical Finance: Discrete ... 阅读全帖 |
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M****i
发帖数: 58 | 19 This kind of equation can be solved by the method of integrating factor.
For your problem, choose the integrating factor z(t)=exp(-w(t)+t/2) and then
use Ito's formula to get d(x(t)z(t))=z(t)dt (this is only an ODE). So that
the solution of your equation is given by
x(t)=z(t)^{-1}(x(0)z(0)+\int_0^t z(s) ds).
In fact, the same idea can be used to sovle the SDEs of the form
dx(t)=f(t,x(t))dt+c(t)x(t)dw(t),
where f and c are continuous functions.
In this general case, the integrating factor is
z(t)... 阅读全帖 |
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A*****s
发帖数: 13748 | 20 Oksendal那本我读起来怎么那么想吐啊，讲个Brownian Motion为什么都非得和泛函扯
到一起？而且符号也用得太heavy了，从某一张pickup，根本没法trace back那一坨一
坨的符号。。。
请推荐比较适合finance application用的SDE书或者讲义，最主要的是要有解American
Option的。谢谢！ |
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r**a
发帖数: 536 | 21 try "arbitrage theory in continuous time" 不过说实话，Oksendal的那本应该已经
很简单了。
American |
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L**********u
发帖数: 194 | 22 Oksendal那本书叫什么名？
这个名字怎么那么熟悉。 但是在电脑上却找不到他的书。
American |
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r**a
发帖数: 536 | 23 I got another solution.
Let Y=X^{-1/2}. Then dY=3/8*Y^{-1}dt-1/2*dB
Now let Z=e^Y. Then
$$
dZ=[Z(\frac{1}{8}+\frac{3}{8\log(Z)})]dt-\frac{Z}{2}dB
$$
Notice that the above eq. regarding Z is in the form of
$$
dZ=f(Z)dt+\frac{Z}{2}dB
$$
Then we may use the result of exersice 5.16 in Oksendal's book "stochastic
differential equations" to solve it. |
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Q***5
发帖数: 994 | 25 You can show that there is a version of B_t that is continous, (I think you
can find a proof in, say, Oksendal's book.), but you can not really proof
that B_t must be continous. |
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l*******z
发帖数: 108 | 27 我看了 Ch3 Oksendahl/Sulem's Applied Stochastic Control of Jump Diffusions 和 Ch 10 Oksendal - Stochastic differential equations (book)(6ed., Springer, 2003)(385s).
如果我没理解错的话，此类问题的应该这样解决。
V(x) = max(tau >= 0) E[int(0,tau) e^(-r t) f(X(t)) dt + e^(-r tau) g(X(tau)) | X(0)=x]
1.求出Characteristic Operator Az
2.作用到g', g'=g+w 得到 Az g'=Ay g+f(y), y(s,x)
3.Domain of U={y;Ay g+f(y)>0}
这里g=0,所以判断条件就是f(y)>0,此题目就是x>a,stopping time exist.且第一次到达X*，应该stop。
下面的问题是怎么求解这个x*？ 好像需要解个ODE，有点类似与 American Style Option W... 阅读全帖 |
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x******a
发帖数: 6336 | 28 1.解一个ode或者pde求出x*,所以你得到了一个极大domain D
2.optimal stopping time就是第一次hit D的边界的时间。u*(x)=E^xu(X_(t_D))
3.有积分多加一个coordinate, 和没积分没有本质区别.
4. RXNT同学注意到这个第一问入手 \rho > \mu 积分难道不是正无穷？
X_0>0的时候，E(|X|)=E(X)=X_0*exp(\mu t)，你可以先看看习题10.17.
和 Ch 10 Oksendal - Stochastic differential equations (book)(6ed., Springer
, 2003)(385s).
)) | X(0)=x]
到达X*，应该stop。
Option Without Maturity的求解，之后怎么做？就不会了 |
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s*****u
发帖数: 164 | 29 Oksendal, Stochastic Differential Equations, Page 76
dY_t = \frac{b-Y_t}{1-t}dt + dB_t, 0<=t<1, Y_0 = a
For your case, a = 0, b = x. |
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