Use of stochastic and mathematical programming in portfolio theory and practice

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Abstract

Standard finance portfolio theory draws graphs and writes equations usually with no constraints and frequently in the univariate case. However, in reality, there are multivariate random variables and multivariate asset weights to determine with constraints. Also there are the effects of transaction costs on asset prices in the theory and calculation of optimal portfolios in the static and dynamic cases. There we use various stochastic programming, linear complementary, quadratic programming and nonlinear programming problems. This paper begins with the simplest problems and builds the theory to the more complex cases and then applies it to real financial asset allocation problems, hedge funds and professional racetrack betting.

Keywords

Portfolio theory Mean-variance analysis Risk aversion Utility function Stochastic programming Capital growth theory 
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Financial Modeling and Stochastic Optimization (Emeritus), Sauder School of BusinessUBCVancouverCanada
  2. 2.Mathematical InstituteOxford UniversityOxfordUK
  3. 3.ICMA CentreUniversity of ReadingReadingUK

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