
on Computational Economics 
By:  Marco Castellani; Emanuel Santos 
Abstract:  This paper evaluates several artificial intelligence and classical algorithms on their ability of forecasting the monthly yield of the US 10year Treasury bonds from a set of four economic indicators. Due to the complexity of the prediction problem, the task represents a challenging test for the algorithms under evaluation. At the same time, the study is of particular significance for the important and paradigmatic role played by the US market in the world economy. Four datadriven artificial intelligence approaches are considered, namely, a manually built fuzzy logic model, a machine learned fuzzy logic model, a selforganising map model and a multilayer perceptron model. Their performance is compared with the performance of two classical approaches, namely, a statistical ARIMA model and an econometric error correction model. The algorithms are evaluated on a complete series of endmonth US 10year Treasury bonds yields and economic indicators from 1986:1 to 2004:12. In terms of prediction accuracy and reliability of the modelling procedure, the best results are obtained by the three parametric regression algorithms, namely the econometric, the statistical and the multilayer perceptron model. Due to the sparseness of the learning data samples, the manual and the automatic fuzzy logic approaches fail to follow with adequate precision the range of variations of the US 10year Treasury bonds. For similar reasons, the selforganising map model gives an unsatisfactory performance. Analysis of the results indicates that the econometric model has a slight edge over the statistical and the multilayer perceptron models. This suggests that pure datadriven induction may not fully capture the complicated mechanisms ruling the changes in interest rates. Overall, the prediction accuracy of the best models is only marginally better than the prediction accuracy of a basic onestep lag predictor. This result highlights the difficulty of the modelling task and, in general, the difficulty of building reliable predictors for financial markets. 
Keywords:  interest rates; forecasting; neural networks; fuzzy logic. 
URL:  http://d.repec.org/n?u=RePEc:ise:isegwp:wp42006&r=cmp 
By:  John Stachurski (Department of Economics, University of Melbourne) 
Abstract:  This paper studies a Monte Carlo algorithm for computing distributions of state variables when the underlying model is a Markov process. It is shown that the L1 error of the estimator always converges to zero with probability one, and often at a parametric rate. A related technique for computing stationary distributions is also investigated. 
Keywords:  Distributions, Markov processes, simulation. 
JEL:  C15 C22 C63 
Date:  2006–04 
URL:  http://d.repec.org/n?u=RePEc:kyo:wpaper:615&r=cmp 
By:  Flam, Sjur (Economics Department, Bergen University); Ruszczynski, A. (Rutgers University, Department of Management Science and Information Systems) 
Abstract:  This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or NikaidoIsoda function is convexconcave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to design computational algorithms for finding such equilibria. To comply with some freedom of individual choice the algorithms developed here are fairly decentralized. However, since coupling constraints must be enforced, repeated coordination is needed while underway towards equilibrium. Particular instances include zerosum, twoperson games  or minimax problems  that are convexconcave and involve convex coupling constraints. 
Keywords:  Noncooperative games; Nash equilibrium; joint constraints; quasivariational inequalities; exact penalty; subgradient projection; proximal point algorithm; partial regularization; saddle points; Ky Fan or NikaidoIsoda functions 
JEL:  C63 C70 
Date:  2006–04–27 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2006_009&r=cmp 
By:  Christiansen, Christian H. (Department of Business Studies); Lysgaard, Jens (Department of Business Studies) 
Abstract:  In this article we introduce a new exact solution approach to the Capacitated Vehicle Routing <p> Problem with Stochastic Demands (CVRPSD). In particular, we consider the case where all customer demands are distributed independently and where each customer’s demand follows a Poisson distribution. The CVRPSD can be formulated as a Set Partitioning Problem. We show that, under the above assumptions on demands, the associated column generation subproblem can be solved using a dynamic programming scheme which is similar to that used in the case of deterministic demands. To evaluate the potential of our approach we have embedded this column generation scheme in a branchandprice algorithm. Computational experiments on a large set of test instances show promising results 
Keywords:  Routing; Stochastic programming; Logistics; Branch and Bound; Dynamic programming 
Date:  2006–03–01 
URL:  http://d.repec.org/n?u=RePEc:hhb:aaracc:92011&r=cmp 
By:  Letchford, Adam N. (Department of Management Science); Lysgaard, Jens (Department of Business Studies); Eglese, Richard W. (Department of Management Science) 
Abstract:  In open vehicle routing problems, the vehicles are not required to return to the <p> depot after completing service. In this paper, we present the first exact optimization <p> algorithm for the open version of the wellknown capacitated vehicle routing problem <p> (CVRP). The algorithm is based on branchandcut. We show that, even though the <p> open CVRP initially looks like a minor variation of the standard CVRP, the integer <p> programming formulation and cutting planes need to be modified in subtle ways. <p> Computational results are given for several standard test instances, which enables <p> us for the first time to assess the quality of existing heuristic methods, and to compare <p> the relative difficulty of open and closed versions of the same problem. 
Keywords:  Vehicle routing; branchandcut; separation 
Date:  2006–04–26 
URL:  http://d.repec.org/n?u=RePEc:hhb:aaracc:92013&r=cmp 
By:  Johansen, Søren Glud (Department of Operations Research); Thorstenson, Anders (Department of Business Studies) 
Abstract:  We study the continuousreview (r; q) system in which un_lled demands are treated <p> as lost sales. The reorder point r is allowed to be equal to or larger than the order <p> quantity q. Hence, we do not restrict our attention to the wellknown case with at most <p> one replenishment order outstanding, but our modeling streamlines exact analysis of that <p> case. The cost structure is standard. We assume that demand is Poisson, that lead <p> times are Erlangian and that orders do not cross in time (lead times are sequential). We <p> determine the equilibrium distribution of the inventory on hand at the delivery instants <p> from the solution (obtained by the GaussSeidel method) of the equilibrium equations of a Markov chain. To optimize r and q we develop an adapted version of the algorithm <p> suggested by Federgruen and Zheng for the backorders model (BO). The results obtained <p> in our numerical study show that the suggested procedure dominates standard textbook <p> approximations. In particular, the reductions in the average cost of a simple Economic <p> Order Quantity policy are in the range of 314%. Except when lead times are long and <p> variable or when the unit cost of shortage is low, the optimal BO policy provides a fair <p> approximation to the average cost of the best policy. 
Keywords:  inventory/production; operating characteristics; policies; probability; Markov processes; Area of review; Manufacturing; Service; Supply Chain Operations 
Date:  2004–10–11 
URL:  http://d.repec.org/n?u=RePEc:hhb:aaracc:92003&r=cmp 
By:  John Stachurski (Department of Economics, University of Melbourne) 
Abstract:  This paper studies fitted value iteration for continuous state dynamic programming using nonexpansive function approximators. A number of nonexpansive approximation schemes are discussed. The main contribution is to provide error bounds for approximate optimal policies generated by the value iteration algorithm. 
Date:  2006–04 
URL:  http://d.repec.org/n?u=RePEc:kyo:wpaper:618&r=cmp 
By:  Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT); Davide La Torre (Department of Economics, Business and Statistics, University of Milan, IT) 
Abstract:  Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L^2 decomposition like the KacSiegert/KarnounenLoeve series.In this paper we first propose a IFSM (Iterated Function Systems with Maps) operator whose fixed point is the trajectory of the BM. We then use this representation of the process to simulate its trajectories. The resulting simulated trajectories are selfaffine, continuous and fractal by construction. This fact produces more realistic trajectories than other schemes in the sense that their geometry is closer to the one of the true BM's trajectories. The IFSM trajectory of the BM can then be used to generate more realistic solutions of stochastic differential equations. 
Keywords:  iterated function systems, Brownian motion, simulation of stochastic differential equations, 
Date:  2006–01–13 
URL:  http://d.repec.org/n?u=RePEc:bep:unimip:1016&r=cmp 