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I guess you must work in finance? It is? QuantNet is a quantitative finance forum. Because finance is so far beneath you?

I guess you must work in finance? Look at the title of the thread. It invited debate on who is the best mathematician. IMHO, it the best result that counts and my impression is that none of Tao's (obviously great) achievements has equaled Perelman's achievement, no matter how many fields he...

He's not that young anymore ;) Nor the best of our time, IMHO (not quite at the level of say Perelman).

Good luck with that. Toronto is not remotely comparable to the US or London, and not just in scale.

I meant "not doable in C#" at a deeper level. In your example, you have the option of avoiding generics (e.g. MatrixDouble, MatrixInt, etc...) at the expense of code maintainability. But it seems the entire concept of arbitrary combinations of objects for the purpose of computation is not...

Interesting. Implicit inlining is relied on more than I realized.

I don't know about that. Genetic programming off the top of my head seems like it could conceivably use arbitrary levels of compositions. In fact, this caught my attention because this is what they were trying to do at the last (FT) job I had: The boss had an idea that objects representing...

You mention no run-time type erasure, but avoiding indirection can be crucial for some applications of compositions. For example, if composition is nested (n-1)-times, e.g. for n=4: auto f_4 = compose(f_3, compose(f_2, compose(f_1, f_0))); then if I am not mistaken you will have 3 levels of...

No, you plugged in z=0 on the RHS. Sorry, you need to be more careful than that ;) We can actually use the same idea as for \(p=\frac12\): Let \(g(z)=\log(f(z))'=\frac{f'(z)}{f(z)}\), which is defined on \([0,1)\) since \(f(0)>0\) as you pointed out earlier. From \(g(z)=pg(pz+q)+qg(qz+p)\), we...

To finish what we started: Given \(0<p<1\), from @zlatancrew we have \(f(z)=f(pz+q)f(qz+p)\qquad(1)\). Assume that \(E[X+Y]=f'(1)<\infty\). @zlatancrew pointed out that we have already proved it for \(p=\frac12\). Let \(\lambda=f'(1)\). As @Hi Rez suggested: Claim 1. \(f^{( n...

I think you are on the right track, and that @Hi Rez is possibly already there: If the pgf \(f\) is also entire, or at least has radius of convergence > 1, then \(f^{( k )}(1)=E[X(X-1)(X-2)...(X-k+1)] = \lambda^k\) would imply that \(f(x)=e^{\lambda(x-1)}\) because they have the same Taylor...

I can't understand why g"(1) must be defined, even for the left derivative (since 1 is not in the interior of the domain)? When we talk about the \(f^{( n )}(1)\) , this uses differentiation of the series defining f term by term.

Good point that b=-a is automatic.

I'm not sure what you mean by "the factorial moments of X are of the form \(\lambda^k\)"?

Looks perfect up to (3) but I couldn't follow the rest. It seems you were close with the idea of using the Identity Theorem. I can do the special case \(p=\frac12\) with the additional assumption that the generating function is an entire function: \(f(z)=f(\frac{z+1}2)^2\qquad\) (4) Then...

Oh, is that so:

He just copy and pasted from Post #4, from 2007.

Actually, the interviewer claimed that "a copy ctor is not generated". If "function body code generation" includes inlined functions, then I believe your quote from the standard, and also your code example, prove him wrong. If the copy ctor is used (i.e. odr-used) then the code is generated for...

So it appears that the interviewer was for the most part correct, though it was a bit of a trick question. An implicit copy constructor is automatically declared but not auto-generated in the sense of an actual compiled function body. Now my understanding is that when a trivial copy constructor...

Another basic test question? I don't recall exactly. After he said the answer was wrong I clarified that it is only generated if the copy constructor is actually called. But he said something about how a copy constructor shouldn't be called because the class should be treated as a struct of...

That's what I said, but the interviewer said I was wrong. Yanking my chain I guess, considering the group.

If a class only has non-const PODs, e.g. class A { int x; double d; }; is a copy-constructor auto-generated?

Sadly, my only quant experience (aside from freelance consulting) has been in Canada. My experiences have been completely at odds with what I read, here and on Wilmott, about being a quant.

You are way off there, because an MFE is not a product. For example, no one worries about consequences or retaliation from writing a bad product review. Also, doing an MFE can have a huge impact on your future (positive or negative). People are not going to be comfortable coming out and saying...

This is probably the most absurd thing I've ever read on this forum. Read up on some history of mathematics if you are interested in the truth. Well, it was for a junior trading role, and I was told they did not want candidates over the age of 25. This is called age discrimination. I'm not...

Age discrimination is rampant in the US based on what I've read (including some examples above). From quant finance forums I gather that it is not as bad in finance as say Silicon Valley. I've been told I'm over the age limit for some jobs in Asia where I guess there are no laws against it...

Some things that I've found useful from C++11: boost::thread has been incorporated into the standard (i.e. std::thread), and even a bit of added language support. Language support for lambda expressions! (I'm not sure how it compares to boost::lambda but I would assume much better.) Range based...

Good point. Self-reported fraudulent placement statistics can also feed these delusions.

Delusional.

11. If you get rejected it could be a big blessing in disguise.

If you are only applying in Toronto, that could be a big problem. I'm doubtful there are many legitimate quant developer roles here. Most of what you read on QuantNet does not apply to the Toronto market. I've seen "quant developers" in senior roles here that are so bad they would be fired...

Yes, that is it. I did not see it under "Your Content" but it's clearly there. I'm glad to hear there is no censorship here (if @Fer Carranza is correct)! I'm not sure how much, but some posts have been deleted at Wilmott by their admin.

I was going to link to a cautionary thread, where a couple of students alleged to have been badly harmed by that program. The point being that you may want to limit spending but also go for a very durable model. I still have my laptop from 5 years ago when I was an MFE student. I can write code...

Some of those numbers are "mistaken".

If anyone cares to give a brief definition of what a unit test is, I would be interested.

It's not clear at all, nor does it look correct. For one thing, the first two sentences appear to violate no free lunch. 1) Presumably your question concerns what is a more attractive for someone selling the option assuming they want to hedge the risk (assuming something like Black-Scholes, the...

Really, you graduated from their program without knowing what a contradiction is?? Not only is there a possible scenario where both of his statements hold true (i.e. no contradition), there is a very plausible hypothesis. It seems that even those in favour of the program are in agreement about...

Wrong. At UFT, the School of Graduate Studies mandates that all academic departments very clearly inform graduate students of appeal procedures in the event of failing certain examinations (definitely PhD comprehensive examination, I forget exactly what the scope is). It is the department's...

Not just any program, the one affiliated with Canada's most prestigious university which also has a high world ranking. Image if the program at MIT or Harvard was exposed as a scam.

Apparently you don't even know what pure math is. There is no financial math there. Also, there is plenty of hand-holding in pure math btw.

Oh, right.:oops:

I had a quick look, and it doesn't really look like open source. You have to pay for their connectivity-plugins. I'm not sure what you can do with them...

I checked the source but got: "This blog is open to invited readers only". I'm not sure if there was more info there. No one has mentioned TradeLink. Any opinions? It all open source, except for their commerical strategy development product Glean which is not necessary. (Unfortunately?)...

Either you are a complete moron, or you passing judgment without even bothering to follow the postings in this thread.

"The Myth of American Meritocracy" is interesting on many levels. It describes corruption in academic admissions, and its cover up, in a very convincing and accessible manner. Based on my first-hand experiences in pure mathematics, it only gets worse as one climbs the academic ladder to...

So you were saying that it is easy to find a (arbitrarily close) distribution approximating sqrt(F_X). I'm no expert on approximating distributions, but I couldn't think of any good alternative solution. The only thing that comes to mind is approximating F_X empirically, as jon hd originally...

You are correct that the solution is not that difficult to understand. The reason I said that you apparently lack mathematical depth is because you claim that approximations of distributions are not hard to come by (presumably you meant the type of approximation we are discussing here). You...

You are a poor sport, by trying to minimize my contribution which I made at your request; everyone knows we have been talking about an approximation all along. You make a claim that series of approximations to distributions are not "hard to come by". Can you point me to any textbook or...

I'm afraid the irony was lost on you. :LOL: You are implying that my hint of how to solve your (very nice I must say) problem was incorrect. But I assure you it is. I said that you can obtain approximations arbitrarily close to the solution. Formally: Claim. There is a transformation mapping...

??? "Poorly endowed". You're completely ignorant, since you know nothing about me. What are your accomplishments in pure mathematics anyways? You've also failed to acknowledge my solution, or stay on topic by discussing it further.

Umm, yes. You think they do something useful? You're welcome for the solution, btw.

I doubt it exists but that is a problem for useless pure mathematicians. You can get an arbitrarily close approximation, without knowing F(x). Hint: What is the Fourier expansion of \(x^{\frac12}\) about 1?

If you look at the original post, he hadn't read the question correctly. (Yes I am arguing with you now:) )

Who was arguing? No one explicitly requested a solution, so I was encouraging the posters to think it out for themselves.

OK. That is an approximate solution, but you can do better and you don't need Fx. Hint: Generators are assumed to produce independent sequences of RV's.

Perhaps it is a difficulty with the English? The point made before was that you are not *given* F(x). Now you are assuming you are given both F(x) and Q(x).

You evidently don't know much about random number generation. I looked at the Python RNG library you referenced. It is a dinky (i.e. basic) generator, that is absolutely not suitable for many financial applications. The reasons for this have been discussed at length on Wilmott. This is coming...

I was simply getting annoyed with Barny posting false statements. He sounds sure of himself, and the problem with is that others reading his posts may be mislead. I was not suggesting that MATLAB is the answer. However, I had in mind professionals in finance who grudgingly shell out for...

You had me worried that perhaps I had spent the last few years improving my skills in the wrong computer language. However, as I expected the Python language is too slow for serious number crunching, apparently by a factor of 10-100x compared with C++...

A number of "facts" you've posted in this thread indicate you don't know what you are talking about (C++ not portable?!). While, I am not familiar with Python, I would bet your above statement is completely false, since it would mean that all of the functionality of all MATLAB toolboxes is...

I can't see the relevance of either of these two. Anyhow much of C++11 functionality was already in boost. But what language are the R algorithms written in? Surely, not R itself? Like I said, I think it depends on what kind of "quant". Unfortunately, I've never had a quant job requiring...

Well, thanks! But I don't think the "ultimate Monte Carlo framework" ever happened (yet), and least not by me. I completed the enhanced random number generators.

I think it depends on the definition of "quant". If things like execution speed and reusability are not a priority then yes something like MATLAB makes more sense. Otherwise, I think you will need a C based language asap.

Exactly, I started with Basic first on a Commodore Pet computer and then on Apple II+. But I really started developing when I began programming in machine language (6502) on the Apple. I wrote a video game with speech back in 1984 (it was in Basic with a lot of machine language subroutines); I'm...

Me?? The OP was claiming he had two methods of solving the problem without using the given generator. I was simply pointing out that he has nothing without the given generator. Yes?

You need to read the question properly. How can you generated anything relevant without the given generator? You are not given F(x).

No. The headhunter I first spoke to referred me to his colleague, who says that the economy there is so bad that I should forgot about a quant job in Japan unless I know someone. I really don't know whether or not he knows what he is talking about ... I once interviewed (unsuccessfully) for a...

According to Wikipedia: "The résumé is comparable to a curriculum vitae (CV) in many countries, although in English Canada, the United States and Australia a résumé is substantially shorter than a CV."

All this time I thought CV was a "British" word for resume (it's Latin I assume, but of course I mean that the term is used instead of resume in the UK and other non-US countries).

From what I've heard, most of the new positions start in May every year (or maybe it was beginning of April at the start of the fiscal year?). Which month is best to be there for quant job interviews?

Your points, unlike mine, are well-expressed. And of course we all know about people like John Nash. Nevertheless, I've spent many years around "real" mathematics (some very good, most not), and even when they are completely irrational their reasoning is not so blatantly faulty as the person I...

That reminds me of my last boss. I tried to explain to him that he was violating the most basic principles of software design (among other things, he used to like copying the same block of code multiple times making minor modifications to each copy -- I'm not sure what this common anti-pattern...

I'm not sure about "most" but it is the case for very many. However, I observed that for most math profs. politics was by far the most important game, with math taking a distant second fiddle.

Sorry if this is a dumb question, but how do I start a new thread on the forum? I looked for 2 minutes and I still don't see how.

I looked at some simple examples, and once I understood them, the documentation on the CMake web page usually suffices. There is also a CMake mailing list, which is an excellent resource for more advanced issues. qfcl/random uses CMake, so you can find example CMakeLists.txt files there, but...

I use the CMake build system. It is a cross-platform build system, but I have found it to be invaluable for project management, including dependencies, even when using MSVS only. I no longer have any need for Property sheets. There is a bit of a learning curve but in my opinion it's more than...

Repost of the solution \(and fixed typos in last paragraph\): Here is a solution in case anyone is interested. If you have a better one, please share... Let \\(B\) be Brownian motion and \\(B_a\) be its reflection at \\(a\): \\(B_a=B\) if \\(a\) has not yet been hit and \\(B_a=2a-B\) after...

I'm not sure if you mean there was a problem with rendering latex? It was formatted correctly at the time it was posted. It looks a bit "cleaned up" from earlier today, but some bits of the solution have gone missing so I will repost it ...

Yup. I'm busy now, but I'll repost it later ...

Andy Nguyen: Perhaps there is some technical problem (e.g. disk failure)? The solution looked find back in March when I posted it...

Pure nonsense. The fact that someone has "studied serious mathematics or physics" in the past, does not imply that they will be familiar with a new branch of math/science.

Toronto. Why do you ask?

My understanding of the OP is that he has to sit in meetings the rest of the workday. Otherwise he would be daft to consider quitting his job.

As Jacek Podlewski showed, under the assumptions on X and Y, ((*)\text{ \quad} E[(X+Y)^2|X=x]=x^2 + 2x E[Y] + E[Y^2]=x^2 + x + \frac13). Here are some more exercises to further your understanding: (1) Let X and Y be as before, but without the assumption that they are independent. Write...

Thanks! That means a lot.

Thanks. I solved it a while ago. My job was terminated recently, giving me time to write up the solution.

Here is a solution in case anyone is interested. If you have a better one, please share... Let (B) be Brownian motion and (B_a) be its reflection at (a): (B_a=B) if (a) has not yet been hit and (B_a=2a-B) after (a) has been hit, which is also Brownian motion by the reflection principle. The...

As far as Canada's biggest university, financial support for graduate students has apparently become a big problem. It was brought to my attention by advertisements in the subway stations.

Here's the policy for our department in case you are interested:

You can do it that way, using PDEs. But, at least for standard Brownian motion, this can be done with just basic probability theory + the reflection principle. I agree that there is probably nothing like a closed form solution, but you can't know that for a fact without formalizing what is...

Yes, and they make an important point that its "not attained automatically as a function of extended experience": "The key is deliberative practice: not just doing it again and again, but challenging yourself with a task that is just beyond your current ability, ..." I work with people who...

Of course it is a matter of personally preference. But, Joshi's account is shorter because is goes straight to the important points. It shows that there is absolutely no need for all those complex integrals in Shreve. Have you checked Bjorn's book (I haven't looked at it recently)? Yes, you...

Yes, I tried as soon as you said "simplify". I meant that there must be some mathematical phenomenon explaining why everything "magically" cancels out.

Yes, I was very surprised when you pointed out that the expression for density of the first passage time for BM with a drift simplifies to \(\frac{m}{\sqrt{2\pi t^3}}e^{-\frac{(m-\alpha t)^2}{2t}}.\) It's not obvious to me why this happens. Maybe Fourier transforms would help? I was just...

I've never heard of Model Validation quants being lumped in with Risk Management quants before, even though MV might in some large group in a bank with "risk management" in its name.

Good review, but I recommend not to look at it until after you've seen the move.

I'm a quant in risk management, but I didn't realize that the non-quants in my group are called "risk managers". Maybe I should update my title on my CV to say more than "Market & Credit Risk Management"? Or maybe it doesn't make a difference, since anyone who reads the content of the CV will...

The intuition is correct, but this is straightforward: The first passage time is the random variable \(\tau_m=\min\{t:X(t)=m\}\). By definition, its cdf is \(P[\tau_m \le T]\), which is equal to \(P[M(T)\le m]\). Whenever the cdf of a random variable is differentiable, the pdf (i.e. the...

Looks like a good one. I'll try it when I have a chance (I work full-time).

No. If \(\tau_a=\min\{t:X(t)=a\}\) is the first passage time of the process \(X\) to \(a\), then the first passage time density is: \(\frac{\partial}{\partial T}\mathrm{P}[\tau_a<T]\). In the case where \(X=W\) is Brownian motion and \(a >0\)...

Nice observation: For all \(k\), \(G(k,k)\) is the complete bipartite graph \(\mathbf{K}_{k,k}\).

You're right about \(k\) (I incorrectly said \(\frac k2\) edges).

peterruse: Your method and equation are correct, but the solution is n=100 not 56. Still, the real question is whether such a Xmas party is mathematically consistent. I appreciate the Xmas spirit, but its easier to talk about graphs: each Santa is a node and a pair of Santas are friends if...

It looks exactly like what I did: Fix one Santa. Each of the 22 Santas connected to the first Santa is connected to 21 other Santas (other than the first and the 22 connected to the first). Then observe that each of these 22 * 21 Santas is being counted exactly 6 times.

Yes, any graph with these properties has exactly 100 nodes. I will explain when I have time. The question (for me) is whether such a graph exists.

IF such a graph exists, I can prove that there must be 100 Santas. But it seems more difficult to prove that there is such a graph with 100 nodes (I'm still thinking about it). It is a trick question if there is no such graph.

This is continued from this thread. A common quant interview question: Let (\tau_a = \min\{t:W(t)=a\}) be the first hitting time of Brownian motion (W(t)) at the level (a). Find (P[\tau_a < T]), in other words probability that BM hits the barrier (a) in time (T). A more challenging question is...

I'm not sure probability you mean, but I'll post the question anyways in case anyone else is interested.

Just curious: I guess there's no such thing as a part-time PhD in Finance?

Okay, its clear now, but its better to use correct mathematical notation/definitions :) I defined two stopping times above, the first time BM hits a and b: Ta = min{t:W(t)=a} Tb = min{t:W(t)=b} There are three possible mutually exclusive events: E1 = {Ta < min(Tb, T)} (a is hit before b...

Your notice is confusing (what is u?). Perhaps you are asking the following interesting question? Let Ta = min{t:W(t)=a} and Tb = min{t:W(t)=b} be the hitting times at a and b. What is P[Ta <= T & Tb <= T], i.e. what is the probability of hitting both barriers in the time interval [0,T]?

First of all, the article is dated: things are different now. Looking at her linkedin profile, she is no longer with DE Shaw and moved to a "client facing" role more recently. Secondly, I would take anything written in the Notices of the AMS with a large grain of salt: Its their propaganda...

I didn't read his question carefully. I thought quotes was asking P(Wt=a) where t is the stopping time. quotes: What are t and T. Is t the stopping time? Are you then asking what P(Wt=a and t < T) for some arbitrary T?

Yes, this is a very basic quant interview question. The formula is trivial, but a proof is a bit nontrivial. Hint: W is a Martingale.

Your belief is a delusion.

Nice. I would personally recommend Eigen, which we are now using in a major production project. It has a very nice C++ interface, and makes effective use of expression templates. Here is performance comparison of a few of the libraries listed, as well as some non-free ones, versus Eigen...

This is a couple of weeks old but I don't think its been posted on Quantnet: David Heath, co-developer of the Heath–Jarrow–Morton framework for Interest rates, passes away Tue, 16 Aug 2011 08:52:00 GMT Public Sad news. Via Biao Guo's Blog comes the news that David Heath has passed away. David...

I tried it again on my dual core laptop at home. The results are now stable but 2 threads are about 50% slower than 1. I tried to close as many other processes as possible in Task Manager, but there are still over 50 processes running (and I can't even do that on my work computer). I am seeing...

I tried using raw pointers instead, but got no improvement (no apparent difference) :( Note that I sometimes (~50%) get linear speedup with 2 threads, but other times it's slower than 1 as above. I'm not sure if you were getting linear speedup consistently? I'm trying a slightly less trivial...

Hi, Thanks for running it. Maybe you meant 10^9? I would be very surprised if a dual core could be more than 1000x slower than my computer (Q9400 @ 2.66GHz). My understanding of MT does not include much beyond your article. For (1), the problem is definitely small in the sense that all of the...

I read the very nice article “C++ Multithreading in Boost” on Quantnet, and tried my own simple example. The n-word checksum of the consecutive integers 0, 1, … is computed. For example, for n = 3 it looks like 0 1 2 3 4 5 6 7 8 : : : The strange thing is, that on a quad-core computer, the...

IMO: Aside from some funny quotes, its full of partial truths, and gives a very distorted view of what its like to be an academic mathematician ...

This can also be shown without doing trigonometric calculations: Let P be the plane containing the base of the pyramid, let T be the top vertex of the pyramid and let U be the vertex of the tetrahedron opposite the pyramid. (1) Observe that TU is parallel to P: Let M1 be the midpoint of the...

See the thread: Nytimes.com to charge for viewing next year

From the same person who just showed me how to read NY Times for free :D

If you are still on the original topic of a game played on an infinite grid, then you are wrong if you mean getting 3 in a row/column. Then as Tsotne mentioned one player has a winning strategy: Alice (1st player, or X) has an easy winning strategy: On her second move she places an X adjacent...

Many thanks everyone for your helpful comments. I ordered the 3rd edition of the Tsay book based on alain's recommendation.

Any suggestions for a good econometrics textbook for modeling financial time series?

I've seen references online to a second edition published in 2009, but it is not available anywhere. Does anyone know what happened?

He's got nothing better to do "On the 1st of January" gives it away...