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on Computational Economics |
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Issue of 2009‒12‒05
twelve papers chosen by |
| By: | Manfred Gilli; Enrico Schumann |
| Abstract: | There is a large number of optimisation problems in theoretical and applied finance that are difficult to solve as they exhibit multiple local optima or are not ‘well- behaved’ in other ways (eg, discontinuities in the objective function). One way to deal with such problems is to adjust and to simplify them, for instance by dropping constraints, until they can be solved with standard numerical methods. This paper argues that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable to handle non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, the paper presents several actual problems where classical methods fail. Next, several well-known heuristic techniques that may be deployed in such cases are described. Since such presentations are quite general, the paper describes in some detail how a particular problem, portfolio selection, can be tackled by a particular heuristic method, Threshold Accepting. Finally, the stochastics of the solutions obtained from heuristics are discussed. It is shown, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations. |
| Keywords: | Optimisation heuristics, Financial Optimisation, Portfolio Optimisation |
| JEL: | C61 C63 G11 |
| Date: | 2009–02–09 |
| URL: | http://d.repec.org/n?u=RePEc:com:wpaper:007&r=cmp |
| By: | Alan G. Isaac |
| Abstract: | This paper refines a well-known set of template models for agent-based modeling and offers new reference implementations. It also addresses issues of design, flexibility, and ease of use that are relevant to the choice of an agent-based modeling platform. |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:amu:wpaper:2009-19&r=cmp |
| By: | Carlo Alberto Magni; Giovanni Mastroleo; Marina Vignola; Gisella Facchinetti |
| Abstract: | Business economics does not provide any methodology for appraising strategic investments, relying on informal approaches. Conversely, financial economics offers us plenty of sophisticated mathematical models unsuitable for applications and based on unrealistic assumptions. This paper presents an example of how strategic investments may be handled with a formal but easy-to-undersand tool. While this paper shows a specific application, a real-life case, we think the model here proposed may be generalized, so contributing to developing a new approach to business decisions. In particular, we think of a fuzzy expert system approach as a convenient tool overwhelming many of the shortcomings inherent in the “crisp” approaches of the financial literature (DCF methods, options pricing, dynamic programming), while avoiding at the same time the refusal of any methodology (typical of business economics). The idea here presented develops some results by Magni et al. (2001) and Facchinetti et al. (2001). An evaluation function is drawn up via “if-then” rules; the latter are made to work automatically by means of an expert system, which adequately replicates the evaluation of human experts. A sensitivity analysis is presented to test the soundness of the model. |
| Date: | 2009–11–16 |
| URL: | http://d.repec.org/n?u=RePEc:col:000162:006122&r=cmp |
| By: | David R.F. Love (Department of Economics, Brock University) |
| Abstract: | The deterministic extended-path method for solving dynamic stochastic optimization problems approximates conditional expectations instead of approximating a model's complex non-linear dynamics. We show that this straightforward approach provides similar accuracy to the best results reported for alternative methods, and gives uniform performance across the entire state space. Our implementation requires roughly 4 fold more computer time than Galerkin projection, but the method has offsetting simplicity and generality that make it an attractive choice. |
| Keywords: | Dynamic stochastic equilibrium, computational methods, non-linear solutions |
| JEL: | E10 E30 E37 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:brk:wpaper:0907&r=cmp |
| By: | Francesco Battaglia; Mattheos Protopapas |
| Abstract: | Many time series exhibit both nonlinearity and nonstationarity. Though both features have often been taken into account separately, few attempts have been proposed to model them simultaneously. We consider threshold models, and present a general model allowing for different regimes both in time and in levels, where regime transitions may happen according to self-exciting, or smoothly varying, or piecewise linear threshold modeling. Since fitting such a model involves the choice of a large number of structural parameters, we propose a procedure based on genetic algorithms, evaluating models by means of a generalized identification criterion. The performance of the proposed procedure is illustrated with a simulation study and applications to some real data. |
| Keywords: | Nonlinear time series; Nonstationary time series; Threshold model |
| Date: | 2009–02–20 |
| URL: | http://d.repec.org/n?u=RePEc:com:wpaper:009&r=cmp |
| By: | E. Obasanjo; G. Tzallas-Regas; B. Rustem |
| Abstract: | We present a primal-dual interior-point method for constrained nonlinear, discrete minimax problems where the objective functions and constraints are not necessarily convex. The algorithm uses two merit functions to ensure progress toward the points satisfying the first-order optimality conditions of the original problem. Convergence properties are described and numerical results provided. |
| Keywords: | Discrete min-max, Constrained nonlinear programming, Primal-dual interior-point methods, Stepsize strategies. |
| Date: | 2009–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:com:wpaper:019&r=cmp |
| By: | Dennis K.J. Lin; Chris Sharpe; Peter Winker |
| Abstract: | The concept of a flexible region describes an infinite variety of symmetrical shapes to enclose a particular region of interest within a space. In experimental design, the properties of a function on the region of interest is analyzed based on a set of design points. The choice of design points can be made based on some discrepancy criterion. This paper investigates the generation of design points on a flexible region. It uses a recently proposed new measure of discrepancy for this purpose, the Central Composite Discrepancy. The optimization heuristic Threshold Accepting is used to generate low discrepancy Utype designs. The proposed algorithm is capable to construct optimal U-type designs under various flexible experimental regions in two or more dimensions. The illustrative results for the two dimensional case indicate that using an optimization heuristic in combination with an appropriate discrepancy measure, it is possible to produce high quality experimental designs on flexible regions. |
| Keywords: | Central composite discrepancy, Experimental design, Flexible regions, Threshold accepting, U-type design |
| Date: | 2009–08–20 |
| URL: | http://d.repec.org/n?u=RePEc:com:wpaper:013&r=cmp |
| By: | P. M. Kleniati; Panos Parpas; Berc Rustem |
| Abstract: | We consider the problem of finding the minimum of a real-valued multivariate polynomial function constrained in a compact set defined by polynomial inequalities and equalities. This problem, called polynomial optimization problem (POP), is generally nonconvex and has been of growing interest to many researchers in recent years. Our goal is to tackle POPs using decomposition. Towards this goal we introduce a partitioning procedure. The problem manipulations are in line with the pattern used in the Benders decomposition [1], namely relaxation preceded by projection. Stengle’s and Putinar’s Positivstellensatz are employed to derive the so-called feasibility and optimality constraints, respectively. We test the performance of the proposed method on a collection of benchmark problems and we present the numerical results. As an application, we consider the problem of selecting an investment portfolio optimizing the mean, variance, skewness and kurtosis of the portfolio. |
| Keywords: | Polynomial optimization, Semidefinite relaxations, Positivstellensatz, Sum of squares, Benders decomposition, Portfolio optimization |
| Date: | 2009–11–10 |
| URL: | http://d.repec.org/n?u=RePEc:com:wpaper:023&r=cmp |
| By: | Yang, Zaigui |
| Abstract: | Assuming that individuals are altruistic, this paper employs an overlapping generations model with lifetime uncertainty to study the partially funded public pension in China. By comparing the market economy equilibrium with the social optimum allocation, we find the optimal firm contribution rate. Our simulation results show that this rate increases when the life expectancy rises, while decreases when the population growth rate falls. It decreases in the joint case of risen life expectancy and fallen population growth rate because it is much more sensitive to the latter than to the former. The result has some policy implications. |
| Keywords: | altruism; lifetime uncertainty; pension contribution rat |
| JEL: | H55 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:18845&r=cmp |
| By: | Gregory de Walque; Olivier Pierrard; Abdelaziz Rouabah |
| Abstract: | This paper develops a dynamic stochastic general equilibrium model with interactions between a heterogeneous banking sector and other private agents. We introduce endogenous default probabilities for both firms and banks, and allow for bank regulation and liquidity injection into the interbank market. Our aim is to understand the importance of supervisory and monetary authorities to restore financial stability. The model is calibrated against real data and used for simulations. We show that liquidity injections reduce financial instability but have ambiguous effects on output fluctuations. The model also confirms the partial equilibrium literature results on the procyclicality of Basel II. |
| Keywords: | DSGE, Banking sector, Default risk, Supervision, Money |
| JEL: | E13 E20 G21 G28 |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:bcl:bclwop:cahier_etudes_35&r=cmp |
| By: | Manfred Gilli; Enrico Schumann |
| Abstract: | This paper details the implementation of binomial tree methods for the pricing of European and American options. Pseudocode and sample programmes for Matlab and R are given. |
| Keywords: | Option pricing, Binomial trees, Numerical methods, Matlab, R |
| JEL: | G13 |
| Date: | 2009–02–15 |
| URL: | http://d.repec.org/n?u=RePEc:com:wpaper:008&r=cmp |
| By: | P. M. Kleniati; Berc Rustem |
| Abstract: | In this paper, we address the global optimization of two interesting nonconvex problems in finance. We relax the normality assumption underlying the classical Markowitz mean-variance portfolio optimization model and consider the incorporation of skewness (third moment) and kurtosis (fourth moment). The investor seeks to maximize the expected return and the skewness of the portfolio and minimize its variance and kurtosis, subject to budget and no short selling constraints. In the first model, it is assumed that asset statistics are exact. The second model allows for uncertainty in asset statistics. We consider rival discrete estimates for the mean, variance, skewness and kurtosis of asset returns. A robust optimization framework is adopted to compute the best investment portfolio maximizing return, skewness and minimizing variance, kurtosis, in view of the worst-case asset statistics. In both models, the resulting optimization problems are nonconvex. We introduce a computational procedure for their global optimization. |
| Keywords: | Mean-variance portfolio selection, Robust portfolio selection, Skewness, Kurtosis, Decomposition methods, Polynomial optimization problems |
| Date: | 2009–11–10 |
| URL: | http://d.repec.org/n?u=RePEc:com:wpaper:021&r=cmp |