<t> Omega IS the set of all possible outcomes of a random experiment. F is a sigma algebra, contained in the power set (category of all subsets) ofOmega and corresponds to the class of all events in the probability space. P is the probability measure that gives the probability of the events in F A r...

<t> I would also recommend John Walkenbach's "Excel 2003 Power Programmingwith VBA". I've found that what a good programmer needs for a new platformor programming model is a solid sequence of simple examples to get familiar with"how things are done" on the new platform. This book is great for that. ...

Is this a basic calculus course? The derivative must be found by the chainrule and is not generally zero. Might be zero at certain points (e.g. whereS'(t) is zero, assuming x is not a function of t)

Impossible? How about: Generate two independent random numbers, x and y, each uniformly distributedon [-1, 1]. Compute D = x^2 + y^2. If D <= 1, use the pair (x,y). Else, reject the pair and tryagain.

<t> I probably did not adequately explain what I meant. I'm not talking aboutnumerical simulations. I intend for this question to be interpreted analytically. Let me give a simple example to illustrate. Consider a standard BrownianMotion, W_t, on [0,T]. Split the interval into two pieces, [0, T/2] a...

<t> I am interested in the following problem. Forgive me if it is a standard problem and I am not seeinghow simple it is. If there is a text which treats this, I would appreciate being directed to it. Let X_t be a continuous stochastic process on some interval [0,T]. Partition the interval by {t_k},...

<t> One project that might be interesting is to see if you can sucessfully identify the "patterns" oftechnical analysis. For example, if you check out the encyclopedia on chart patterns by ThomasBulkowski, you find a lot of supposed chart patterns like "Broadening Bottoms" and "Bump andRun Reversal ...

<t> Far be it from me to downplay the importance of making money, but the real point is to comeup with a valid and reliable model of market behavior. Presumably, a better model could alsobe used profitably. The basic plain-vanilla market model is geometric Brownian motion (GBM), which is unbeatablef...

<t> I'll take a stab at this. I would say that, generally, 1) and 4) are synonomous. High Frequency trading refers to intradaytrading, on the time scale of minutes and even seconds. Statistical arbitrage is a broad term forbuy-side methodologies that attempt to generate alpha by looking for statisti...

<t> But it clearly makes no sense. Suppose that we had selected the other envelope first, rather than theone with $100. The host opened that envelope, showing us that it containedeither $50 or $200. Then, by the exact same rational, the clear choice wouldbe to switch to the other envelope, i.e. the ...

<t> Hence the paradox. You have probabilty of 1/2 of having selected the highestamount already. You can't improve that by switching. So how can the otherenvelope be preferred over the one you have selected? You haven't gotten any new information: you already knew there was *some*dollar value in the ...

<t>QuoteOriginally posted by: LepperbeA lot easier to grasp with only 2 envelopes in stead of 3 doors Answer depends on your risk aversion though...(do you prefer $100 over a 50/50 chance of getting $50 or $200)Behavioral finance even suggest the answer depends on whether you receive the money in th...

<t> Or more to the point, the probability that you picked the right door thefirst time out is 1/3; the probability that it is behind one of the two doorsthat you did not pick is 2/3. The host just showed you which of the other doors it is *not* behind,if indeed it is behind one of them. So there is ...

<t> This is indeed an old problem, called the Monty Hall problem. [Check Wikipedia for the story] It roseto prominence in the early 90's when it was featured in a column by Marilyn vos Savant -- who waspurported to have the highest IQ ever measured -- and it became the subject of widespread debate. ...

<t> I am curious if anyone knows a quick method for approximating (even numerically)the cdf/pdf of a non-normal distribution. In particular, that of a distribution with mean,variance, skewness and kurtosis [perhaps higher moments] whose the values indicateit is not normal. [I would like to be able t...