publication . Other literature type . Article . Preprint . 2018

A General Framework for Portfolio Theory—Part I: Theory and Various Models

Maier-Paape, Stanislaus; Zhu, Qiji Jim;
  • Published: 08 May 2018
  • Publisher: MDPI AG
  • Country: Germany
Abstract
Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz [H. Markowitz, Portfolio Selection, 1959] and its natural generalization, the capital market pricing model, [W. F. Sharpe, Mutual fund performance , 1966] are special cases of our general framework when the risk measure is taken to be the standard deviation and the utility function is the identity mapping. Using our general framework...
Subjects
free text keywords: 330, Markowitz portfolio theory, capital market pricing model, convex programming, efficient frontier, financial mathematics, fractional Kelly allocation, growth optimal portfolio, risk measure, utility functions, Quantitative Finance - Portfolio Management, 52A41, 90C25, 91G99, Replicating portfolio, Portfolio, Investment theory, Mathematical economics, Modern portfolio theory, Actuarial science, Capital asset pricing model, Economics, Portfolio optimization, Spectral risk measure, ddc:330
Related Organizations

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[25] J. L. Treynor, Toward a theory of market value of risky assets. Unpublished manuscript 1962. A nal version was published in 1999, in Asset Pricing and Portfolio Performance: Models, Strategy and Performance Metrics. Robert A. Korajczyk (editor) London: Risk Books, pp. 1522.

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publication . Other literature type . Article . Preprint . 2018

A General Framework for Portfolio Theory—Part I: Theory and Various Models

Maier-Paape, Stanislaus; Zhu, Qiji Jim;