Portfolio Optimization by Means of Multiple Tandem Certainty-Uncertainty Searches

Portfolio Optimization by Means of Multiple Tandem Certainty-Uncertainty Searches: A Technical Description

Brian G. Chow
Copyright Date: 2013
Published by: RAND Corporation
Pages: 70
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  • Book Info
    Portfolio Optimization by Means of Multiple Tandem Certainty-Uncertainty Searches
    Book Description:

    This paper describes a new approach to optimization under uncertainty that is aimed at finding the optimal solution to a problem by designing a number of search algorithms or schemes in a way that allows analysts to apply to a problem that contains a significantly larger number of decision variables, uncertain parameters, and uncertain scenarios than they have had to contend with until now.

    eISBN: 978-0-8330-8295-4
    Subjects: Technology, History

Table of Contents

  1. Front Matter
    (pp. i-ii)
  2. Preface
    (pp. iii-iv)
  3. Summary
    (pp. v-x)
  4. Abbreviations
    (pp. xi-xii)
  5. Acknowledgments
    (pp. xiii-xiv)
  6. Chapter One: Introduction
    (pp. 1-8)

    Nikolaos Sahinidis classified the theory and methodology that have been developed to cope with the complexity of optimization problems under uncertainty into three main approaches.²Stochastic programmingcovers the two-stage uncertainty programming paradigm in which the first-stage variables are those that have to be decided upon before the actual realization of the uncertain parameters at the second stage in the future. The second category isfuzzy mathematical programming. Unlike stochastic programming, fuzzy programming allows constraints to be violated within some lower and upper bounds. The third category isstochastic dynamic programming, which deals with multistage decision processes. The approach proposed...

  7. Chapter Two: Technical Description
    (pp. 9-32)

    This chapter describes the approach. It starts by discussing the basic ideas that underlie it. It next provides a mathematical formulation of the portfolio optimization process. It then discusses the two specific ideas that underlie the approach: (1) the use of multiple algorithms to search for the optimal portfolio (OP) and (2) a new process to design algorithms. It then describes the steps for any given search scheme (SS), the specific steps for eight SSs, and flow charts illustrating the common SS approach and two variants. Next, it discusses OPs and products to produce them. Finally, it describes two methods...

  8. Chapter Three: Applications of the Approach in Past Studies
    (pp. 33-40)

    As noted above, applications of this approach were developed in theToward Affordable Systemsseries of studies that were sponsored by the Deputy Assistant Secretary of the Army (Cost and Economic Analysis), Office of Assistant Secretary of the Army (Financial Management and Comptroller).⁵² In this chapter, how the approach was applied in two of those cases from the past studies is discussed.

    The first case is an application that appeared inToward Affordable Systems II.⁵³ The purpose of this application is to decide how much money should be spent on the science and technology (S&T) projects that are already existing...

  9. Chapter Four: Overview of the Approach and Suggestions forExpanding Its Use
    (pp. 41-44)

    The combinatorial possible solutions of problems under uncertainty grow exponentially with the number of decision variables, uncertain parameters, and uncertain scenarios. Even the most powerful computers cannot perform exhaustive searches in a reasonable amount of time when they are faced with an exponential growth of possible solutions. Yet the popular stochastic programming approaches use exhaustive searches to take advantage of pioneered works of Dantzig and Beale in decomposing the uncertainty problem into solvable, deterministic (certainty) linear programming problems.

    The approach described here proposes to sample the uncertainty space with typically 10,000 FSWs. It takes advantage of the fact that once...

  10. Appendix: Embodiments of Computer Resources Used in Portfolio Optimization by Means of Multiple Certainty-Uncertainty Searches
    (pp. 45-52)
  11. Bibliography
    (pp. 53-56)