nep-cmp New Economics Papers
on Computational Economics
Issue of 2007‒09‒24
three papers chosen by
Stan Miles
Thompson Rivers University

  1. NLINLS: a Differential Evolution based nonlinear least squares Fortran 77 program By Mishra, SK
  2. How to Determine the Order-up-to Level When Demand is Gamma Distributed with Unknown Parameters By Janssen, E.; Strijbosch, L.W.G.; Brekelmans, R.C.M.
  3. Sparse and Stable Markowitz Portfolios By Brodie, Joshua; Daubechies, Ingrid; De Mol, Christine; Giannone, Domenico

  1. By: Mishra, SK
    Abstract: This paper provides the list of Fortran 77 codes of nonlinear least squares using Differential Evolution as the minimizer algorithm. It has been tested on a number of difficult nonlinear least squares problems (taken from NIST, USA including CPC-X Software challenge problems). Help on how to use the program also is provided.
    Keywords: Nonlinear least squares; Differential Evolution; Fortran 77
    JEL: C8
    Date: 2007–08–25
  2. By: Janssen, E.; Strijbosch, L.W.G.; Brekelmans, R.C.M. (Tilburg University, Center for Economic Research)
    Abstract: Inventory models need information about the demand distribution. In practice, this information is not known with certainty and has to be estimated with often relatively few historical demand observations. Using these estimates leads to underperformance. This paper focuses on gamma distributed demand and a periodic review, order-up-to inventory control policy, where the order-up-to level satisfies a service equation. Under this policy the underperformance is quantified analytically under strong assumptions and with help of simulation if these assumptions are relaxed. The analytical results can be used to improve the attained service level, such that it approaches the desired service level more closely, even if the assumptions are not met. With help of simulation we show that in some cases this improvement results in reaching the desired service level. For the remaining cases, i.e., the cases in which the desired service level is not reached, the underperformance decreases; improvements range from almost 17% up to over 90%. Moreover, with help of simulation and linear regression further improvements can be obtained. The desired service level is reached in more cases and the underperformance in the other cases is decreased even more compared to using only the first improvement. These improvements range from 57% up to 99% compared to the base case (i.e., do not use analytical results) and from 35% up to over 90% compared to using the analytical results, except for a few cases in which the service hardly improved, but in those cases the attained service level was already very close to the desired one. Finally, the method developed in this paper is applied to real demand data using simulation. The total improvements in this case study range from 53% up to 96%.
    Keywords: Unknown Demand Parameters;Inventory Control;Gamma Distribution;Ser- vice Level Criterion;Case Study
    JEL: C13 C53
    Date: 2007
  3. By: Brodie, Joshua; Daubechies, Ingrid; De Mol, Christine; Giannone, Domenico
    Abstract: The Markowitz mean-variance optimizing framework has served as the basis for modern portfolio theory for more than 50 years. However, efforts to translate this theoretical foundation into a viable portfolio construction algorithm have been plagued by technical difficulties stemming from the instability of the original optimization problem with respect to the available data. In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of a penalty proportional to the sum of the absolute values of the portfolio weights (l1 penalty). This penalty stabilizes the optimization problem, encourages sparse portfolios, and facilitates treatment of transaction costs in a transparent way. We implement this methodology using the Fama and French 48 industry portfolios as our securities. Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the naïve portfolio comprising equal investments in each available asset. In addition to their excellent performance, these portfolios have only a small number of active positions, a highly desirable attribute for real life applications. We conclude by discussing a collection of portfolio construction problems which can be naturally translated into optimizations involving l1 penalties and which can thus be tackled by algorithms similar to those discussed here.
    Keywords: Penalized Regression; Portfolio Choice; Sparse Portfolio
    JEL: C00 G11
    Date: 2007–09

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