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Large scale portfolio optimization with piecewise linear transaction costs

Large scale portfolio optimization with piecewise linear transaction costs,10.1080/00207160802263858,Optimization Methods & Software,Marina Potaptchik

Large scale portfolio optimization with piecewise linear transaction costs   (Citations: 3)
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We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model for the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle the non-smoothness in the objective function by using spline approximations. The problem is first solved approximately using a primal-dual interior-point method applied to the smoothed problem. Then, we crossover to an active set method applied to the original non-smooth problem to attain a high accuracy solution. Our numerical tests show that we can solve large scale problems efficiently and accurately.
Journal: Optimization Methods & Software - OPTIM METHOD SOFTW , vol. 23, no. 6, pp. 929-952, 2008
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    • ...In [12, 23, 25, 27] transaction costs are modeled as linear or piecewise linear functions...

    E. G. Birginet al. Low order-value approach for solving VaR-constrained optimization prob...

    • ...variance portfolio optimization with piecewise linear transaction costs, [2] and [18] pro-...
    • ...jective. On the other hand, in [18], interior point method is used (in locating the initial...
    • ...methods do. To get the merits from both methods, [18] proposed a cross-over method: in...
    • ...Strategy proposed in [18] is designed to deal with a convex program with an objective...
    • ...(4.7) (for some xed " > 0)) can be computed eciently. [18] proposed that...
    • ...[18] proposed the above cross-over technique in the setting of convex program, and the...

    Yuen-Lam Cheung. Portfolio Optimization via Downside-Risk Aversion Model

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