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EnglishWe consider the following problem. A set r(1), r(2),..., r(K)is an element of R(T) of vectors is given. We want to find the convex combination z = Sigma lambda(j) r(j) such that the statistical median of z is maximum. In the application that we have in mind, r(j), j = 1, ..., K are the historical return arrays of asset j and lambda(j), j = 1, ..., K are the portfolio weights. Maximizing the median on a convex set of arrays is a continuous non-differentiable, non-concave optimization problem and it can be shown that the problem belongs to the APX-hard difficulty class. As a consequence, we are sure that no polynomial time algorithm can ever solve the model, unless P=NP. We propose an implicit enumeration algorithm, in which bounds on the objective function are calculated using continuous geometric properties of the median. Computational results are reported.
The optimal statistical median of a convex set of arrays. / S. Benati; R. Rizzi. - In: JOURNAL OF GLOBAL OPTIMIZATION. - ISSN 0925-5001. - STAMPA. - 44:1(2009), pp. 79-97.
| Titolo: | The optimal statistical median of a convex set of arrays. | |
| Autori: | ||
| Data di pubblicazione: | 2009 | |
| Rivista: | ||
| Citazione: | The optimal statistical median of a convex set of arrays. / S. Benati; R. Rizzi. - In: JOURNAL OF GLOBAL OPTIMIZATION. - ISSN 0925-5001. - STAMPA. - 44:1(2009), pp. 79-97. | |
| Abstract: | We consider the following problem. A set r(1), r(2),..., r(K)is an element of R(T) of vectors is given. We want to find the convex combination z = Sigma lambda(j) r(j) such that the statistical median of z is maximum. In the application that we have in mind, r(j), j = 1, ..., K are the historical return arrays of asset j and lambda(j), j = 1, ..., K are the portfolio weights. Maximizing the median on a convex set of arrays is a continuous non-differentiable, non-concave optimization problem and it can be shown that the problem belongs to the APX-hard difficulty class. As a consequence, we are sure that no polynomial time algorithm can ever solve the model, unless P=NP. We propose an implicit enumeration algorithm, in which bounds on the objective function are calculated using continuous geometric properties of the median. Computational results are reported. | |
| Handle: | http://hdl.handle.net/11562/409558 | |
| Appare nelle tipologie: | 01.01 Articolo in Rivista |
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