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by gumpleon
February 11th, 2008, 6:11 am
Forum: Brainteaser Forum
Topic: The Test Taker
Replies: 7
Views: 61985

The Test Taker

i disagree. all exam results are correlated: good students tend to be good at all exams. the multiplication needs the independent assumption, which does not hold here.
by gumpleon
January 22nd, 2008, 9:30 pm
Forum: Brainteaser Forum
Topic: another card game
Replies: 22
Views: 72081

another card game

<t>the numeric procedure to solve this problem is to use the dynamic algorithm to backtrack the all possible states. it is sort of like the binomial tree but the probability of up/down is changing along the way. the best strategy is then to pick a new card if the expected pay of the move is larger t...
by gumpleon
January 22nd, 2008, 5:39 pm
Forum: Brainteaser Forum
Topic: Maximum permutations
Replies: 7
Views: 62696

Maximum permutations

then the maximum m is be n!: it is to visit all possible states of the string reordering.
by gumpleon
January 11th, 2008, 6:20 pm
Forum: Brainteaser Forum
Topic: Uniform distribution and two points
Replies: 8
Views: 64145

Uniform distribution and two points

<t>for b, two commonly used estimators are MLE and MOM (of course, other estimators are possible as well): b_{MLE} = X_{max}, and b_{MOM} = X_1 + X_2.MLE is biased while MOM unbiased. the key is about how to assess the goodness of estimators. usually we use mean square error to evaluate estimators. ...
by gumpleon
January 10th, 2008, 11:14 pm
Forum: Brainteaser Forum
Topic: A question from Goldman Sachs interview
Replies: 11
Views: 68036

A question from Goldman Sachs interview

<t>QuoteOriginally posted by: VassiliOption A has half option B's value. That's a restatement of the 'reflection principle.'Actually, we don't exactly know the price ratio because S is a geometric BM. With zero interest and divident, log(S) is a BM with downward trend. The reflective principle does ...
by gumpleon
November 14th, 2007, 6:12 am
Forum: The Quantitative Finance FAQs Project
Topic: How can I simulate correlated random numbers?
Replies: 34
Views: 296569

How can I simulate correlated random numbers?

<t>Quote Hi, I have same question as you. Do you have any solution now? I am eager to know your answer soon. Thanks!Theoretically, it is to compute the conditional distribution of the random variables conditioned on those known ones. For normal cases, the analytic solution of the conditional distrib...
by gumpleon
October 8th, 2007, 9:55 pm
Forum: The Quantitative Finance FAQs Project
Topic: What is convexity?
Replies: 34
Views: 278724

What is convexity?

<t>QuoteOriginally posted by: drdConvexity, at its root, means curvature, and ONLY curvature. In the case of non-contingent IR products, it has NOTHING to do with volatility or anything else, as such. It is purely a property of the pricing formulas. However, as there are many aspects in finance and ...
by gumpleon
September 17th, 2007, 2:36 am
Forum: Student Forum
Topic: which instrument to use, future, option or swap?
Replies: 3
Views: 65643

which instrument to use, future, option or swap?

thanks for the replies. it clarifies the issues for me.
by gumpleon
September 9th, 2007, 6:55 pm
Forum: Student Forum
Topic: which instrument to use, future, option or swap?
Replies: 3
Views: 65643

which instrument to use, future, option or swap?

<t>suppose a fund manager plans to hedge the company's financial portfolio, and various common instruments are out there. the question is how the manager determines which instrument is the right one to use. in other words, what are the pro and cons of these instruments?i know all instruments well (a...
by gumpleon
June 14th, 2007, 3:39 am
Forum: Student Forum
Topic: Box-Jenkins
Replies: 2
Views: 70287

Box-Jenkins

<t>QuoteOriginally posted by: tibbarIf fitting a CIR model to historic data only (I'm using it to model dividend yields), would it be reasonable to use a time series approach where dt = 1 day and then apply Box-Jenkins estimation?You need to check the model assumption. Likely it won't work because A...
by gumpleon
June 14th, 2007, 3:37 am
Forum: Student Forum
Topic: Box-Jenkins
Replies: 2
Views: 70287

Box-Jenkins

<t>QuoteOriginally posted by: tibbarIf fitting a CIR model to historic data only (I'm using it to model dividend yields), would it be reasonable to use a time series approach where dt = 1 day and then apply Box-Jenkins estimation?You need to check the model assumption. Likely it won't work because A...
by gumpleon
June 14th, 2007, 3:34 am
Forum: Student Forum
Topic: Basic chain rule question.
Replies: 14
Views: 70951

Basic chain rule question.

QuoteWhat is dF/dG where:F = E[ f(X) ]G = E[ X ]E[ ] is expectation,X is any random variable.It is not right because both F and G are just two numbers.Furthermore, the original question is ill-posed because F is a function of G in general.
by gumpleon
March 7th, 2007, 9:35 pm
Forum: Brainteaser Forum
Topic: football score
Replies: 17
Views: 79858

football score

<t>we can also use the reflective principle to do the counting.let N be the difference of games brazil won and german won, the status of the game canbe denoted as a pair (t, N). given brazil won the first game, the number of total possiblepaths is C(13,6). the game starts at (1,1), and ends at (14,2...
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