Universal Portfolio Selection: Application of Information Theory in Finance - SC500 Project Presentation -. Gudrun Olga Stefansdottir May 5 2007. Outline. Introduction Information Theory in Gambling Information Theory and the Stock Market Concepts and Terminology
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Gudrun Olga Stefansdottir
May 5 2007
We can represent the Theory in Financestock market as a vector of stocks
m: Number of stocks
Xi: Price relatives, ratio of price of stock i at the end of the day to the beginning.
x F(x): Joint distribution of the vector of price relatives
Portfolio: Allocation of wealth accross various stocks.
where bi is the fraction of wealth allocated to stock i.The Stock Market
Example: Alice has wealth $100 and her portfolio consists of the following fractions: 50% in IBM, 25% in Disney, 25% in GM
Example: Alice has wealth $100 and she plans to keep it CRP.
Day1: Alice makes her initial investment action, she buys 50% in IBM, and 50% in BAC.
End of Day1: IBM ↑2% $51, BAC ↓1% $49.50. Wealth has increased to $100.50. Needs to sell $0.75 in IBM to buy BAC.
Day2: Alice has adjusted her portfolio to the original fractions.
“A universal online portfolio selection strategy “
for every stock market sequence and for every n, where is the wealth generated by the best constant rebalanced portfolio in hindsight.
So what is the catch???
Value line: Equal proportion invested in each stock in the portfolio (market average)
Wealth relative: Relative increase in wealth if entire money invested in that particular stock.
12/14/1993-12/06/1995 – 500 days Theory in Finance
Increased volatility, x8 Theory in Finance
Mathematics parallel to the mathematics of data compression
If the text in question results in wealth then bits can be saved in a naturally associated deterministic data compression scheme.
where is log-optimal strategy corresponding to f(x) and is the log-optimal strategy corresponding to g(x).