Reference for elementary and "cool" statistics or financial math 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 :-)
The closest I could come up with (using ideas of a friend) is some game theoretic stuff like  price of anarchy  (a related and possibly with much simpler mathematics is  The Economics of Caste and of the Rat Race and Other Woeful Tales  by Akerlof),  Arrow's Impossibility Theorem, and possibly some  Prospect theory.  
Does anyone have any idea about elementary interesting math related to Statistics or Finance?
 A: 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. 
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. 
A: Robert Aumanns theorem on agreeing-to-disagree (the original article can be found here) 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 here. 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.
A: You might consider looking at the binomial asset pricing model. A good-looking book is here.
A: "Efficient Algorithms for Universal Portfolios" http://jmlr.csail.mit.edu/papers/volume3/kalai02a/kalai02a.pdf
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.
A: At the high school level, perhaps they would be interested in the Monty Hall Problem -- that kept me stumped for a while.
A: One topic that I would cover is the St. Petersburg Game (or paradox). 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.)
Good luck.
A: 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. 
http://en.wikipedia.org/wiki/Capital_asset_pricing_model
Hope it helps
