most recent 30 from http://mathoverflow.net 2013-06-19T03:27:16Z http://mathoverflow.net/feeds/question/11497 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11497/reference-for-elementary-and-cool-statistics-or-financial-math auniket 2010-01-12T03:31:45Z 2010-01-21T16:26:07Z

<p>I signed up for a Math Mentorship Program (for high school students) this term, but one of the students assigned to me is more interested in Statistics and Finance - something that would help him to do business :-)</p> <p>The closest I could come up with (using ideas of a friend) is some game theoretic stuff like <a href="http://theory.stanford.edu/~tim/papers/routing.pdf" rel="nofollow"> price of anarchy </a> (a related and possibly with much simpler mathematics is <a href="http://go2.wordpress.com/?id=725X1342&amp;site=gravityandlevity.wordpress.com&amp;url=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DqlwRG3WP4dsC%26pg%3DPA39" rel="nofollow"> The Economics of Caste and of the Rat Race and Other Woeful Tales </a> by Akerlof), <a href="http://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem" rel="nofollow"> Arrow's Impossibility Theorem</a>, and possibly some <a href="http://en.wikipedia.org/wiki/Prospect_theory" rel="nofollow"> Prospect theory</a>. </p> <p>Does anyone have any idea about elementary interesting math related to Statistics or Finance?</p>

http://mathoverflow.net/questions/11497/reference-for-elementary-and-cool-statistics-or-financial-math/11499#11499 Steve Huntsman 2010-01-12T03:44:14Z 2010-01-12T03:44:14Z

<p>You might consider looking at the <a href="http://en.wikipedia.org/wiki/Binomial%5Foptions%5Fpricing%5Fmodel" rel="nofollow">binomial asset pricing model</a>. A good-looking book is <a href="http://www.amazon.com/Stochastic-Calculus-Finance-Binomial-Pricing/dp/0387401008" rel="nofollow">here</a>.</p>

http://mathoverflow.net/questions/11497/reference-for-elementary-and-cool-statistics-or-financial-math/11500#11500 Douglas Zare 2010-01-12T04:00:40Z 2010-01-12T04:00:40Z

<p>I recommend against game theory and prospect theory. This is a high school student who probably won't be used to distinguishing between normative models and descriptive models, and the result might be that he picks up jargon without understanding anything useful. That could be practice for business, but not satisfying for you, I hope. </p> <p>A fundamental question in financial math is how to evaluate a security which pays you $1/year forever, a "perpetuity." I would start there. You only need high school algebra to approach this. You can add inflation and risk, and then get into basic statistical analysis, options pricing (use simple discrete models with no calculus), etc. </p>

http://mathoverflow.net/questions/11497/reference-for-elementary-and-cool-statistics-or-financial-math/11501#11501 Wilson 2010-01-12T04:08:49Z 2010-01-12T04:08:49Z

<p>"Efficient Algorithms for Universal Portfolios" <a href="http://jmlr.csail.mit.edu/papers/volume3/kalai02a/kalai02a.pdf" rel="nofollow">http://jmlr.csail.mit.edu/papers/volume3/kalai02a/kalai02a.pdf</a></p> <p>An algorithm for investing in a portfolio of stocks that guarantees you do almost as well as the best stock in hindsight. Very cool and not super complicated.</p>

http://mathoverflow.net/questions/11497/reference-for-elementary-and-cool-statistics-or-financial-math/11511#11511 Michael Greinecker 2010-01-12T07:37:28Z 2010-01-12T07:37:28Z

<p>Robert Aumanns theorem on agreeing-to-disagree (the original article can be found <a href="http://www.math.huji.ac.il/raumann/pdf/Agreeing%20to%20Disagree.pdf" rel="nofollow">here</a>) is a fun result that can be motivated by simple puzzles. Moreover, it is the basis of the no-trade-theorems in finance that show that rational expectations rule out speculative trading. A leisurely introduction to this, Aumann's theorem, and related issues can be found <a href="http://cowles.econ.yale.edu/~gean/art/p0828.pdf" rel="nofollow">here</a>. This article also motivates these issues in terms of a puzzle for children. I think it should be possible to select some topics that are (at some level) understandable by someone in high school. Moreover, this is a topic that raises questions and gives no answers, so you will not indoctrinate your student.</p>

http://mathoverflow.net/questions/11497/reference-for-elementary-and-cool-statistics-or-financial-math/12526#12526 The Bridge 2010-01-21T11:07:51Z 2010-01-21T11:07:51Z

<p>You might try a simplified version the CAPM with an application regarding the choice of a utility based portfolio on the (Markowitz) Efficient Frontier of market portfolios. It uses concepts of arbitrages, utility functions, portfolio of assets with gaussian yields and all this is quite illuminating. </p> <p><a href="http://en.wikipedia.org/wiki/Capital_asset_pricing_model" rel="nofollow">http://en.wikipedia.org/wiki/Capital_asset_pricing_model</a></p> <p>Hope it helps</p>

http://mathoverflow.net/questions/11497/reference-for-elementary-and-cool-statistics-or-financial-math/12528#12528 Douglas S. Stones 2010-01-21T11:19:35Z 2010-01-21T11:19:35Z

<p>At the high school level, perhaps they would be interested in the <a href="http://en.wikipedia.org/wiki/Monty%5FHall%5Fproblem" rel="nofollow">Monty Hall Problem</a> -- that kept me stumped for a while.</p>

http://mathoverflow.net/questions/11497/reference-for-elementary-and-cool-statistics-or-financial-math/12550#12550 Highgamma 2010-01-21T16:26:07Z 2010-01-21T16:26:07Z

<p>One topic that I would cover is the St. Petersburg Game (or <a href="http://en.wikipedia.org/wiki/St.%5FPetersburg%5Fparadox" rel="nofollow">paradox</a>). Daniel Bernoulli's solution is the basis for expected utility theory and the rivalry between himself and his cousin Nicolas just makes it more fun. (The problem is well-suited to a visual description as well.)</p> <p>Good luck.</p>