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Improvement of the Performance of “Universal Portfolios” Using Techniques of “Universal Source Coding”

Nemati, Sajjad | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43230 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aref, Mohammad Reza; Aminzadeh Gohari, Amin
  7. Abstract:
  8. In this thesis, following a short introduction to investment problem, this problem is investigated with both probabilistic and universal approach. Using the concept of the set of reference algorithms, we present a mathematical definition for universality. We then give examples of universal algorithms for investment and prove their universality. These algorithms are:
    Universal Portfolios without Side Information, Universal Portfolios with Side Information, Universal Portfolios with Semi-Constant Rebalanced Portfolio, Universal Portfolios with Switching.
    We then present a new algorithm called “Universal Portfolio with Multiple Side Information Sources”. This algorithm is applied in situations when the investor has access to multiple sources of side information, but he/she does not know which one is the better. The algorithm attempts to find the best source of side information. We then present the necessary and sufficient conditions for existence of universal portfolios and apply these conditions to the algorithms already studied. We see that the sufficient condition is derived using an upper bound on the performance of the universal algorithm, and this upper bound can be used as measure to find the ultimate limit for improvement of the performance of these universal algorithms
  9. Keywords:
  10. Universal Portfolios ; Multiple Sources of Side Information ; Average Exponential Growth Rate for Investment Algorithm ; Necessary and Sufficient Condition for Existance of Universal Portfolios

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