Integer programming approaches in mean-risk models

Konno, Hiroshi; Yamamoto, Rei

doi:10.1007/s10287-005-0038-9

Cited by 29 publications

(17 citation statements)

References 10 publications

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“…The literature offers a large variety of heuristics and metaheuristics for portfolio selection problems (see, for instance, Chang et al [4], Jobst et al [8] and Mansini and Speranza [13] and more recently Konno and Yamamoto [11]). The heuristics tend to be problem-dependent and, thus, not easily extendable to other, even if very similar, problems.…”

Section: Introductionmentioning

confidence: 99%

Kernel Search: a new heuristic framework for portfolio selection

2010

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In this paper we propose a new heuristic framework, called Kernel Search, to solve the complex problem of portfolio selection with real features. The method is based on the identification of a restricted set of promising securities (kernel) and on the exact solution of the MILP problem on this set. The continuous relaxation of the problem solved on the complete set of available securities is used to identify the initial kernel and a sequence of integer problems are then solved to identify further securities to insert into the kernel. We analyze the behavior of several heuristic algorithms as implementations of the Kernel Search framework for the solution of the analyzed problem. The proposed heuristics are very effective and quite efficient. The Kernel Search has the advantage of being general and thus easily applicable to a variety of combinatorial problems.

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Section: Introductionmentioning

confidence: 99%

Kernel Search: a new heuristic framework for portfolio selection

2010

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“…Kim et al [67] consider a MAD model with both transaction costs and minimum transaction lots, while [77] considers a more general model with cardinality constraints and propose an algorithm to solve the resulting mixed integer linear program.…”

Section: Mad Under Transaction Costsmentioning

confidence: 99%

Mean-Variance Portfolio Optimization : Eigendecomposition-Based Methods

Mayambala¹

2015

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Modern portfolio theory is about determining how to distribute capital among available securities such that, for a given level of risk, the expected return is maximized, or for a given level of return, the associated risk is minimized. In the pioneering work of Markowitz in 1952, variance was used as a measure of risk, which gave rise to the wellknown mean-variance portfolio optimization model. Although other mean-risk models have been proposed in the literature, the mean-variance model continues to be the backbone of modern portfolio theory and it is still commonly applied. The scope of this thesis is a solution technique for the mean-variance model in which eigendecomposition of the covariance matrix is performed.The first part of the thesis is a review of the mean-risk models that have been suggested in the literature. For each of them, the properties of the model are discussed and the solution methods are presented, as well as some insight into possible areas of future research.The second part of the thesis is two research papers. In the first of these, a solution technique for solving the mean-variance problem is proposed. This technique involves making an eigendecomposition of the covariance matrix and solving an approximate problem that includes only relatively few eigenvalues and corresponding eigenvectors. The method gives strong bounds on the exact solution in a reasonable amount of computing time, and can thus be used to solve large-scale mean-variance problems.The second paper studies the mean-variance model with cardinality constraints, that is, with a restricted number of securities included in the portfolio, and the solution technique from the first paper is extended to solve such problems. Near-optimal solutions to large-scale cardinality constrained mean-variance portfolio optimization problems are obtained within a reasonable amount of computing time, compared to the time required by a commercial general-purpose solver.v Populärvetenskaplig sammanfattningFör den som har kapital att investera kan det vara svårt att avgöra vilka investeringar som är mest fördelaktiga. Till stöd för beslutet kan matematiska modeller användas och denna avhandling handlar om hur man kan beräkna lösningar till sådana modeller. De investeringsalternativ som betraktas är finansiella instrument som är föremål för daglig handel, som aktier och obligationer.En investerare placerar kapital i finansiella instrument eftersom de förväntas ge en god avkastning över tiden. Samtidigt är sådana placeringar alltid förknippade med risktagande. Förväntad avkastning och risk varierar kraftigt mellan olika instrument. Till exempel ger placeringar i statsobligationer typiskt mycket låg avkastning till mycket låg risk, medan placeringar i aktier i nystartade bolag som utvecklar nya läkemedel kan ge mycket hög avkastning samtidigt som risken är mycket hög.Att investera kan ses som en avvägning mellan den förväntade avkastningen och den risk som investeringen innebär, och typiskt är hög förväntad avkastning också associerade med e...

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“…[[b solve the problem (2,9), we apply an integer programming approach and Yamarnoto [12]. Hence most xit which satisfy these conditions are expected to be xio in an optimal solution [20].…”

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confidence: 99%