Network techniques for solving asset diversification problems in finance

In this paper, we study a problem of asset diversification or dynamic portfolio selection arising in the field of finance. This problem is first formulated as a nonlinear mathematical program and is solved via a special-purpose computer code that exploits the underlying network structure. A second m...

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Published inComputers & operations research Vol. 9; no. 3; pp. 173 - 195
Main Authors Golden, Bruce L., Keating, Karen D.
Format Journal Article
LanguageEnglish
Published New York Elsevier Ltd 1982
Pergamon Press Inc
Subjects
Assets
Computer based modeling
Diversification
Mathematical programming
Network management systems
Networks
Operations research
Portfolio management
Problem solving
Techniques
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Abstract In this paper, we study a problem of asset diversification or dynamic portfolio selection arising in the field of finance. This problem is first formulated as a nonlinear mathematical program and is solved via a special-purpose computer code that exploits the underlying network structure. A second model for asset diversification is presented which is linear in the decision variables and is therefore much easier to solve computationally than the first formulation. On the other hand, the linear model produces solutions that are consistently inferior to those generated by the nonlinear program in terms of expected profit. This trade-off of accuracy versus efficiency is discussed and assessed for several sample problems. Extensive computational results are presented.
AbstractList In this paper, we study a problem of asset diversification or dynamic portfolio selection arising in the field of finance. This problem is first formulated as a nonlinear mathematical program and is solved via a special-purpose computer code that exploits the underlying network structure. A second model for asset diversification is presented which is linear in the decision variables and is therefore much easier to solve computationally than the first formulation. On the other hand, the linear model produces solutions that are consistently inferior to those generated by the nonlinear program in terms of expected profit. This trade-off of accuracy versus efficiency is discussed and assessed for several sample problems. Extensive computational results are presented.
The ideas from mathematical programming and network optimization can be brought together to solve a dynamic asset diversification problem - in particular, the dynamic portfolio selection arising in the field of finance - in order to maximize total return over a fixed planning horizon. Two problem formulations, a non-linear program and a linear program, are used. The nonlinear mathematical program is solved with a special-purpose computer code that exploits the underlying network structure. The other model is linear in the decision variables. Both models have advantages and disadvantages. The linear model is much easier and less time-consuming to solve computationally. However, its solutions are consistently inferior to those generated by the nonlinear program in terms of expected profit. Thus, a tradeoff of accuracy versus efficiency exists. The financial planner must decide which method is appropriate. Solving both programs by the repeated use of a longest path algorithm over an acyclic network is a possibility.
Author Golden, Bruce L.
Keating, Karen D.
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McCarl, Moskowitz, Furtan (BIB13) 1977; 5
Karlin (BIB8) 1959; Vol. 1
Keating (BIB9) 1981
Markowitz (BIB11) 1952; 7
Kennington, Helgason (BIB10) 1980
Zangwill (BIB18) 1969
Wallingford (BIB17) 1967; 3
Sharpe (BIB14) 1963; 9
Everett (BIB4) 1963; 11
Markowitz (BIB12) 1959
Boot (BIB2) 1964
Sharpe (BIB15) 1971; 6
Stone (BIB16) 1973; 8
Golden (BIB6) 1975; 5
Hazell (BIB7) 1971; 53
Bell (BIB1) 1974; 2
Goldberger (BIB5) 1964
Stone (10.1016/0305-0548(82)90017-X_BIB16) 1973; 8
Bell (10.1016/0305-0548(82)90017-X_BIB1) 1974; 2
Wallingford (10.1016/0305-0548(82)90017-X_BIB17) 1967; 3
Keating (10.1016/0305-0548(82)90017-X_BIB9) 1981
Kennington (10.1016/0305-0548(82)90017-X_BIB10) 1980
Goldberger (10.1016/0305-0548(82)90017-X_BIB5) 1964
Busacker (10.1016/0305-0548(82)90017-X_BIB3) 1965
Zangwill (10.1016/0305-0548(82)90017-X_BIB18) 1969
Karlin (10.1016/0305-0548(82)90017-X_BIB8) 1959; Vol. 1
Markowitz (10.1016/0305-0548(82)90017-X_BIB12) 1959
Sharpe (10.1016/0305-0548(82)90017-X_BIB15) 1971; 6
Golden (10.1016/0305-0548(82)90017-X_BIB6) 1975; 5
Markowitz (10.1016/0305-0548(82)90017-X_BIB11) 1952; 7
Hazell (10.1016/0305-0548(82)90017-X_BIB7) 1971; 53
Boot (10.1016/0305-0548(82)90017-X_BIB2) 1964
Everett (10.1016/0305-0548(82)90017-X_BIB4) 1963; 11
McCarl (10.1016/0305-0548(82)90017-X_BIB13) 1977; 5
Sharpe (10.1016/0305-0548(82)90017-X_BIB14) 1963; 9
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Snippet In this paper, we study a problem of asset diversification or dynamic portfolio selection arising in the field of finance. This problem is first formulated as...
The ideas from mathematical programming and network optimization can be brought together to solve a dynamic asset diversification problem - in particular, the...
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SubjectTerms Assets
Computer based modeling
Diversification
Mathematical programming
Network management systems
Networks
Operations research
Portfolio management
Problem solving
Techniques
Title Network techniques for solving asset diversification problems in finance
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