  The purpose of this paper is to showcase trading strategies that give
solutions to three difficult and intriguing problems in business finance,
economics and statistics. The paper discusses trading strategies for both
commodities and stocks but the main focus is on stock market trading at the New
York Stock Exchange.
  Problem 1: Buy Low and Sell High. The buy low and sell high problem can be
summarized like this: suppose the price of a commodity or stock fluctuates
indefinitely, is there any explicit strategy for a trader to "ride the price
waves" by buying low and selling high to eventually win even if price does not
increase?
  Problem 2: "Beat" the Market. In Part 2, the trading system presented in Part
1 is transformed into a strategy that always outperforms the market eventually.
  Problem 3: Can a Trader Outperform a geometric Brownian Motion? The general
belief is that it is impossible to "beat" a GBM since technical analysis of
historical prices is useless in predicting future prices. The last part of the
paper shows that the answer to Problem 3 is actually a "YES", which is quite
surprising.
  The trading strategies presented are based mainly on information obtained
from the movements of waves and wavelets created by large and small
fluctuations of market prices. They do not involve any forecasting or
prediction of future prices. Behavioral economics also plays a role in the
decision making process of the Wavelet Trading program. My website
AgateTrading.com is available to the public.
