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Mean-risk optimization for index tracking
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Yumiharu Nakano
Published/Copyright:
September 25, 2009
SUMMARY
This paper presents an analysis of the tracking problems of multiple indices with multidimensional performance criterion consisting of mean wealth and the tracking errors. We evaluate the performance of portfolios via the vector inequalities defined by convex cones, which enable us to describe various preference relations for investors. In Brownian market models with deterministic coefficients, we completely determine the set of efficient portfolios as well as the efficient frontier in our context. As a product of our analysis, we exhibit a version of Tobin's mutual fund theorem.
Key words and phrases: portfolio management; index tracking; multicriteria optimization; efficient frontier; mean-risk analysis; mutual fund theorem; risk measures
:
Received: 2005-December-19
Accepted: 2006-March-20
Published Online: 2009-09-25
Published in Print: 2006-07
© R. Oldenbourg Verlag, München
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Keywords for this article
portfolio management;
index tracking;
multicriteria optimization;
efficient frontier;
mean-risk analysis;
mutual fund theorem;
risk measures
Articles in the same Issue
- Editorial preface
- Risk measurement with equivalent utility principles
- Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals
- On distortion functionals
- Convex risk measures and the dynamics of their penalty functions
- Law invariant convex risk measures for portfolio vectors
- Robust utility maximization in a stochastic factor model
- Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints
- On the optimal risk allocation problem
- Monetary utility over coherent risk ratios
- Mean-risk optimization for index tracking
