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on Computational Economics |
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Issue of 2011‒02‒12
nine papers chosen by |
| By: | Oleg Kudryavtsev (INRIA Rocquencourt - MATHFI - INRIA - Ecole des Ponts ParisTech - Université Paris-Est) |
| Abstract: | In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski\v{i} (Finance Stoch. 13: 531--562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one -- the Post-Widder formula. We prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations. |
| Keywords: | Lévy processes; barrier options;regime switching models; Wiener-Hopf factorization; Laplace transform; numerical methods; numerical transform inversion |
| Date: | 2010–01–26 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:inria-00450291&r=cmp |
| By: | Pierre Del Moral (INRIA Bordeaux - Sud-Ouest - ALEA - INRIA - Université de Bordeaux - CNRS : UMR5251); Peng Hu (INRIA Bordeaux - Sud-Ouest - ALEA - INRIA - Université de Bordeaux - CNRS : UMR5251); Nadia Oudjane (LAGA - Laboratoire d'Analyse, Géométrie et Applications - CNRS : UMR7539 - Université Paris-Nord - Paris XIII, EDF R&D - EDF); Bruno Rémillard (MQG - Méthodes Quantitatives de Gestion - HEC-Montréal) |
| Abstract: | We analyze the robustness properties of the Snell envelope backward evolution equation for the discrete time optimal stopping problem. We consider a series of approximation schemes, including cut-off type approximations, Euler discretization schemes, interpolation models, quantization tree models, and the Stochastic Mesh method of Broadie-Glasserman. In each situation, we provide non asymptotic convergence estimates, including Lp-mean error bounds and exponential concentration inequalities. We deduce these estimates from a single and general robustness property of Snell envelope semigroups. In particular, this analysis allows us to recover existing convergence results for the quantization tree method and to improve significantly the rates of convergence obtained for the Stochastic Mesh estimator of Broadie-Glasserman. In the second part of the article, we propose a new approach using a genealogical tree approximation of the reference Markov process in terms of a neutral type genetic model. In contrast to Broadie-Glasserman Monte Carlo models, the computational cost of this new stochastic particle approximation is linear in the number of sampled points. Some simulations results are provided and confirm the interest of this new algorithm. |
| Keywords: | Snell envelope; optimal stopping; American option pricing; genealogical trees; interacting particle model |
| Date: | 2010–05–28 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:inria-00487103&r=cmp |
| By: | V. SELS; F. STEEN; M. VANHOUCKE |
| Abstract: | In this paper, a new procedure to solve a job shop scheduling problem at a Belgian manufacturer producing industrial wheels and castors in rubber is presented. The procedure is an extension of a hybrid shifting bottleneck procedure with a tabu search algorithm while incorporating various company specific constraints. The various extensions to cope with the company specific constraints have a strong similarity with the complex job shop problem formulation of Mason et al. (2002). The new procedure is used as a simulation engine to test the relevance of various scenarios in order to improve the current planning approach of the company. A detailed computational experiment highlights the main contribution of the novel procedure for the company. |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:rug:rugwps:10/678&r=cmp |
| By: | V. SELS; K. CRAEYMEERSCH; M. VANHOUCKE |
| Abstract: | This paper presents a genetic algorithm and a scatter search procedure to solve the well-known job shop scheduling problem. In contrast to the single population search performed by the genetic algorithm, the scatter search algorithm splits the population of solutions in a diverse and high-quality set to exchange information between individuals in a controlled way. Extensions from a single to a dual population by taking problem specific characteristics into account can be seen as a stimulator to add diversity in the search process, which has a positive influence on the important balance between intensification and diversification. Computational experiments verify the benefit of this diversity on the effectiveness of the meta-heuristic search process. Various algorithmic parameters from literature are embedded in both procedures and a detailed comparison is made. A set of standard instances is used to compare the different approaches and the best obtained results are benchmarked against heuristic solutions found in literature. |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:rug:rugwps:10/679&r=cmp |
| By: | Luca Di Corato (Swedish University of Agricultural Sciences); Michele Moretto (University of Padova, Fondazione Eni Enrico Mattei and Centro Studi Levi-Cases); Sergio Vergalli (University of Brescia and Fondazione Eni Enrico Mattei) |
| Abstract: | In this paper stochastic dynamic programming is used to investigate habitat conservation by a multitude of landholders under uncertainty about the value of environmental services and irreversible development. We study land conversion under competition on the market for agricultural products when voluntary and mandatory measures are combined by the Government to induce adequate participation in a conservation plan. We analytically determine the impact of uncertainty and optimal policy conversion dynamics and discuss different policy scenarios on the basis of the relative long-run expected rate of deforestation. Finally, some numerical simulations are provided to illustrate our findings. |
| Keywords: | Optimal Stopping, Deforestation, Payments For Environmental Services, Natural Resources Management |
| JEL: | C61 D81 Q24 Q58 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2010.160&r=cmp |
| By: | V. SELS; N. GHEYSEN; M. VANHOUCKE |
| Abstract: | In this paper, a comparison and validation of various priority rules for the job shop scheduling problem under different objective functions is made.<br> In a first computational experiment, 30 priority rules from literature are used to schedule job shop problems under two flow time-related and three tardiness-related objectives. Based on this comparative study, the priority rules are extended to 13 combined scheduling rules in order to improve the performance of the currently bestknown rules from literature. Moreover, the best performing priority rules on each of these five objective functions are combined into hybrid priority rules in order to be able to optimize various objectives at the same time.<br> In a second part of the computational experiment, the robustness on the relative ranking of the performance quality is checked for the various priority rules when applied on larger problem instances, on the extension of multiple machines possibilities per job as well as on the introduction of sequence-dependent setup times. Moreover, the influence of dynamic arrivals of jobs has also been investigated to check the robustness on the relative ranking of the performance quality between static and dynamic job arrivals. The results of the computational experiments are presented and critical remarks and future research avenues are suggested. |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:rug:rugwps:10/680&r=cmp |
| By: | VAN VYVE, Mathieu (Université catholique de Louvain, CORE and Louvain School of Management, B-1348 Louvain-la-Neuve, Belgium) |
| Abstract: | The fixed-charge transportation problem is an interesting problem in its own right. This paper further motivates its study by showing that it is both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem. We then provide a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path. We give a O(n^3)-time optimization algorithm and two O(n^2)-size linear programming extended formulation. We describe a new class of inequalities that we call "path-modular" inequalities. We give two distinct proofs of their validity. The first one is direct and crucially relies on sub- and super- modularity of an associated set function. The second proof is by showing that the projection of one of the extended linear programming formulations onto the original variable space yields exactly the polyhedron described by the path- modular inequalities. Thus we also show that these inequalities suffice to describe the convex hull of the set of feasible solutions. We finally report on computational experiments comparing extended LP formulation, valid inequalities separation and a standard MIP solver. |
| Keywords: | mixed-integer programming, lot-sizing, transportation, convex hull, extended formulation |
| Date: | 2010–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2010068&r=cmp |
| By: | Marina Murat; Tommaso Pirotti |
| Abstract: | This paper presents a new method for measuring the attractiveness of countries for FDI. A ranking is built using a fuzzy expert system whereby the function producing the final evaluation is not necessarily linear and the weights of the variables, usually defined numerically, are replaced by linguistic rules. More precisely, weights derive from expert opinions and from econometric tests on the determinants of countries’ FDI. As a second step, the view-point of investors from two different investing economies, the UK and Italy, are taken into account. Country-specific factors, such as the geographic, cultural and institutional distances existing between the investing and the partner economies are included in the analysis. This shows how the base ranking changes with the investor’s perspective |
| Keywords: | foreign direct investments; fuzzy expert systems; attractiveness; |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:mod:depeco:0640&r=cmp |
| By: | CHEVALIER, Philippe (Université catholique de Louvain, CORE and Louvain School of Management, B-1348 Louvain-la-Neuve, Belgium); VAN DEN SCHRIECK, Jean - CHristophe (Université catholique de Louvain, CORE and Louvain School of Management, B-1348 Louvain-la-Neuve, Belgium); WEI, Ying (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium) |
| Abstract: | This paper introduces a novel way to measure the variability of order flows in supply chains, the peakedness. The peakedness can be used to measure the variability assuming the order flow is a general point pro- cess. We show basic properties of the peakedness, and demonstrate its computation from real-time continuous demand processes, and cumulative demand collected at fixed time intervals as well. We also show that the peakedness can be used to characterize demand, forecast, and inventory variables, to effectively manage the variability. Our results hold for both single stage and multistage inventory systems, and can further be extended to a tree-structured supply chain with a single supplier and multiple retailers. Furthermore, the peakedness can be applied to study traditional inventory problems such as quantifying bullwhip effects and determining safety stock levels. Finally, a numerical study based on real life Belgian supermarket data verifies the effectiveness of the peakedness for measuring the order flow variability, as well as estimating the bullwhip effects. |
| Keywords: | variability, peakedness, supply chain |
| Date: | 2010–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2010067&r=cmp |