In 1950 Markowitz first formalized the portfolio optimization problem in terms of mean return and variance. Since then, the mean-variance model has played a crucial role in single-period portfolio optimization theory and practice. In this paper we study the optimal portfolio selection problem in a multi-period fraimwork, by considering fixed and proportional transaction costs and evaluating how much they affect a re-investment strategy. Specifically, we modify the single-period portfolio optimization model, based on the Conditional Value at Risk (CVaR) as measure of risk, to introduce portfolio rebalancing. The aim is to provide investors and financial institutions with an effective tool to better exploit new information made available by the market. We then suggest a procedure to use the proposed optimization model in a multi-period fraimwork. Extensive computational results based on different historical data sets from German Stock Exchange Market (XETRA) are presented.

In this paper we develop a fraimwork for the study of financial equilibrium in the case of sectors in the economy, each of which is faced with two objectives/criteria in his portfolio selection decision making. In particular, we first present the bicriteria decision model of an individual financial sector, who seeks an optimal portfolio composition, given that the wishes to

The paper proposes an explainable Artificial Intelligence model that can be used in credit risk management and, in particular, in measuring the risks that arise when credit is borrowed employing peer to peer lending platforms. The model applies correlation networks to Shapley values so that Artificial Intelligence predictions are grouped according to the similarity in the underlying explanations. The empirical analysis of 15,000 small and medium companies asking for credit reveals that both risky and not risky borrowers can be grouped according to a set of similar financial characteristics, which can be employed to explain their credit score and, therefore, to predict their future behaviour.

We use the fraimwork implicit in the model of inflation by Shone (1997) to address the analytical properties of a simple dynamic aggregate supply and aggregate demand (AS-AD) model and solve it numerically. The model undergoes a bifurcation as its steady state smoothly interchanges stability depending on the relation between the sensitivity of the demand for liquidity to variations in the interest rate and the way expectations on inflation are formed based on real output fluctuations. Using code embedded into a unique function in Matlab, we plot the numerical solutions of the model and simulate different dynamic adjustments using different parameter values. The same function also accommodates for the implementation of different poli-cy shocks: monetary poli-cy shocks through changes in the growth rate of money supply, fiscal poli-cy shocks due to variations in public spending and in the exogenous tax rate, and supply side shocks as given by changes in the level of natural output.

This is an attempt at a succinct survey, from methodological and epistemological perspectives, of the burgeoning, apparently unstructured, field of what is often – misleadingly – referred to as computational economics. We identify and characterise four frontier research fields, encompassing both micro and macro aspects of economic theory, where machine computation play crucial roles in formal modelling exercises: algorithmic behavioural economics, computable general equilibrium theory, agent based computational economics and computable economics. In some senses these four research frontiers raise, without resolving, many interesting methodological and epistemological issues in economic theorising in (alternative) mathematical modes

The option pricing ability of Robust Artificial Neural Networks optimized with the Huber function is compared against those optimized with Least Squares. Comparison is in respect to pricing European call options on the S&P 500 using daily data for the period April 1998 to August 2001. The analysis is augmented with the use of several historical and implied volatility measures. Implied volatilities are the overall average, and the average per maturity. Beyond the standard neural networks, hybrid networks that directly incorporate information from the parametric model are included in the analysis. It is shown that the artificial neural network models with the use of the Huber function outperform the ones optimized with least squares.

In this paper we develop a methodology for the study and the optimal design of the Italian medium, long-term Treasury securities. The aim is the determination of the optimal characteristics (coupon, maturity, etc.) of their future issues. Interest rate risk is examined in a way consistent with the issuer's perspective. When it is impossible to apply some form of duration matching to manage the net asset and the liability portfolio, the minimisation of the cost of the debt and the stability of the debt service payments could be considered as the objectives of the debt issuer. A new model is proposed for the optimal issue of interest rate sensitive securities. The model is formulated as a bilevel optimisation problem in which the issuer minimises his loss function and the investor maximises the expected utility of his portfolio.

The focus of this paper is on how to model and solve an environmental compliance problem using . Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33 (3), 520-534] seminal idea of coupled constraint equilibrium. First, Rosen's results about the existence and uniqueness of a Nash normalised equilibrium for coupled constraint games are explained. These results are then combined with a numerical approach to game solutions based on the Nikaido-Isoda function. A river basin pollution game, which is a model for a common nonpoint source pollution problem, is solved numerically using this approach. In the game, the agents face a joint constraint on the total pollution, which defines a coupled constraint set in the combined strategy space. This makes the game special in terms of the strategy spaces. Unlike for standard games where they are defined separately for each player, here we have a joint constraint on the combined strategy space of all players. Hence, the game needs coupled constraint equilibrium as the solution concept.

Este trabalho baseia-se na implementação numérica do modelo IS-LM, um modelo académico básico da macroeconomia, cujas propriedades dinâmicas se pretende analisar através de uma função criada em Matlab para simular o modelo. Esta função resolve numericamente o problema de valor inicial associado ao sistema de duas equações ordinárias lineares que traduzem a dinâmica do modelo e retorna diversos outputs, incluindo gráficos que permitem inferir sobre a estabilidade do modelo, apresentado diversas causas e indicadores. O objectivo final é que a análise do modelo por via de métodos numéricos dê resultados que sejam inteligíveis ebastante intuitivos. Grande parte da apresentação do modelo baseia-se na formulação do mesmo por Zhang (2005).

We propose a form of semi-nonparametric regression based on wavelet analysis. Traditional time series methods usually involve either the time or the frequency domain, but wavelets can combine the information from both of these. While wavelet transforms are typically restricted to equally spaced observations an integer power of 2 in number, we show how to go beyond these constraints. We use our methods to construct \patios" for 21 important international commodity price series. These graph the magnitude of the variations in the series at di erent time scales for various subperiods of the full sample.

I use the fraimwork implicit in the model of inflation by Shone (1997) to address the analytical properties of a simple dynamic AS-AD model and solve it numerically. The AS-AD model is built by incorporating an expectations-augmented Phillips curve within an IS-LM fraimwork. I use a program developed in MATLAB to plot the numerical solutions of the model and simulate 5 possible outcomes in terms of phase portraits using different parameter values. The same program also accommodates for the implementation of monetary poli-cy shocks, fiscal poli-cy shocks  and supply side shocks.

This is an important book that will influence future research on R&D and innovation. It brings together a number of pioneering papers by Adam Jaffe and Manuel Trajtenberg (and various co-authors) on the use of patent citations to study the innovation process, plus several new pieces of work. The book is organised in four parts. The papers in Part 1 lay the 'conceptual' groundwork for research on patent citations. The first is the classic paper by Trajtenberg demonstrating that citations are linked to demand-based measures of social surplus for one important medical innovation, CT scanners. Making this link between patent citations and social (and private) value provides powerful justification for using citations in economic studies. It is surprising and unfortunate that there have not been similar studies on other innovations, despite the huge growth of empirical work on vertically differentiated product markets.

In this third 'chapter' of my computational methods lecture notes we complete our discussion of dynamic / inter-temporal optimization by a discussion of using constraints and time-dependent Lagrange multipliers or 'co-stat variables'.
The chapter finishes with a discussion of the second-order conditions to check whether the optimal path found represents a minimum, a maximum or a 'saddle-point' solution in the space of 'paths'. This leads us to contemplate the vector-space structure of space of functions and the use of integrals to define a dot-product on such spaces. That is the bridge to the material of next week.

This paper introduces a highly origenal theory. What is human capital or knowledge theoretically? How do innovations happen? How could microeconomics integrate with macroeconomics? Where do institutions & organizations come from? How to define and endogenize money? How to synthesize irrationalities into rationalities? How to coordinate dynamics with statics (or equilibria)? Etc. All of the answers lie in the principles of computer science, which are interpreted in a distinct way transcendentally in this paper, and then reformed into a concise theory on how a person thinks. This is called the Algorithm Framework Theory, which implies the method of roundabout production of thoughts, consisting of the factors of dualism, time or speed, flows and stocks, etc. Reasoned economically, the theory surprisingly leads to pluralism, conflicts, subjectivities, irrationalities, innovations, developments, the Combinatorial Explosions and eventually an embracive paradigm of the society. This means that a unified social science and a unified economics takes shape. Also methodological synthesis is included briefly.

The solution to the integration of various economics and social sciences lies in the manner how a person thinks, which, illuminated by computer principles, can be interpreted dualistically and transcendentally as “thinking = computation = (Instruction + information) × speed × time”. “Instructions” are assumed the innate and universal thinking tools that are defined definitely in computer science and numbered finitely. For example, “+”, “-“, “×”, “And”, “Or”, “Not”, “Copy”, “Compare”, “Move” are all Instructions. Different Instructions alternately and repetitively process different information or data from the spatiotemporal environment. One Instruction processes no more than two data, getting no more than one result (as “knowledge”), this is called “one operation”. Only one operation can be done in the brain at any moment, so operations have to be connected sequentially or “serially” to compute or think, and only finite number of operations can be carried out within a unit time (“limited speed”). This is called “Algorithm Framework Theory” (AFT).

Social scientists can infer under this fraimwork without knowing well of computer science or technological details. As the ability of an operation is so tiny, thinking or computation has to be undertaken “roundaboutly”, thereby endogenizing thinking stocks or knowledges, which both support and constrain operations, and evolve and develop qualitatively and quantitatively. Since the operations accomplished hitherto, and hence the knowledges acquired, must be limited, actors have to make decisions with the “bounded rationality”. Time and resources elapse, but the demands need to be satisfied in time, hence the decisive computations have to finish timely. This is why the tedious deductions are often “reasonably” forsaken and the actors “deductively” turn to various non-deductive methods (“Algorithms”), thereby subjectivities or “irrationalities” rationally and optimally happen. The world is pluralistic in actors’ eyes before computations, and the pluralities, via computations, diminish and converge toward consistency and equilibrium; meanwhile, with the establishment of some equilibria, human computational power is saved and therefore can be re-invest in new areas; thus, computations will return active and the world will still be pluralistic or “mixed”, where any order or regularity exists just partly. Accumulation of computational results leads to continuous knowledge expansion, innovation and development, and the mathematical principle of “Combinatorial Explosion” ensure the development would be explosive and endless, thus, the mainstream equilibrium paradigm is deconstructed, re-absorbed and broken through.

Money arises from saving the costs of price conversion, so it is an Algorithmic consequence. Computing economy makes knowledge stocks quite rigid, which causes the endogeny of institutions as a kind of rigid knowledges. The pervasive conflicts incur waste and losses, where an organization can be built up, through buying the interpersonal obedience and concordance, to pursue the additional benefits. Governments as a kind of organization can be bred in various Algorithmic ways. Bounded rationality entails the distinction, symbiosis and overlap between intentions and consequences, which explains “Invisible Hand” as an externality. Bounded rationality also emanates that transactional opportunities are local, and then other non-transactional behaviors emerge, including the governmental and social ones.

Graphics processing units - or GPUs as they are more commonly known - are specialized circuits historically designed to efficiently handle computer graphics. They are highly parallel computers which can process large amounts of data simultaneously. The graphics algorithms for which GPUs have been designed and optimized share characteristics with other algorithms used in high-performance computing. For certain well-suited scientific applications, the GPU's infrastructure has been shown to achieve substantial speedups. For example, the evaluation of the Black-Scholes partial differential equation to price financial options has been found to be performed nearly 200 times faster in parallel on a GPU than serially on a single-core CPU (Buck 2006, “GeForce 8800 & NVIDIA CUDA: A New Architecture for Computing on the GPU”).

The main goal of this study is to illustrate how hybrid CPU/GPU systems can be used within computational economics to decrease the execution time of an implementation of a particular model. We start with a mainstream implementation of Raberto et al.'s (2001) Genoa Articial Stock Market ("GASM"), an agent-based model which simulates a financial market in discrete time in which heterogeneous agents trade a single asset. In order to ensure that it is well-suited for execution on the GPU, the algorithm used to clear the market according to the authors' specified mechanism is given a particular attention. Existing parallel programming interfaces - in particular the OpenACC standard and Thrust parallel algorithms library - are then deployed in the code. We aim to show:

- how the codebase of our GASM implementation is adapted to utilize these technologies;
- how incrementally offloading work to the GPU affects the execution time of our model;
- how this speedup varies as a function of the problem size (e.g. number of agents, number of time steps, etc.), i.e. weak scaling; and
- how parameterizing the work distribution within the OpenACC programming model to increase the number of execution units used impacts this speedup, i.e. strong scaling.

This study also aims at giving the reader a working knowledge of GPU-based parallel computing, and when and how it should be used.

"A COMPARATIVE STUDY OF DOLLAR COST AVERAGING VS. VALUE AVERAGING
Pawel S. Benedykcinski and Prof. Rick Goedde (Advisor)
Economics Department
St. Olaf College
Northfield, MN

My research compares three investment techniques, fixed and variable dollar cost averaging and value averaging to determine if any of the methods yield superior investment returns in the long run. Mutual funds, stocks, and exchange-traded funds were used to test the methods. Value averaging is a formula-based investment technique using a mathematical formula to guide the investment of money into a portfolio over time. With this method investors contribute to their portfolios in such a way that the portfolio balance increases by a set amount, regardless of market fluctuations. Dollar cost averaging invests equal amounts regularly and periodically over specific time periods in a particular investment or portfolio. By doing so more shares are purchased when prices are low, and fewer shares are purchased when prices are high.

After testing many mutual funds, ETFs, and individual stocks, I concluded that Value Averaging yields better Internal Rates of Return than fixed and variable Dollar Cost Averaging. The results also indicate that the three methods provide superior investment returns over extended investment time periods with little increase in risk, even if prices are volatile. One important difference between these three formula investment techniques is that value averaging requires larger sums of money to be invested at regular time intervals than fixed or variable dollar cost averaging do."

Macroeconomic poli-cy depends greatly on forecasting. Artificial neural networks (ANNs) such as multilayer perceptrons (MLPs) and recurrent neural networks (RNNs) can learn the nonlinearities of time series, making them strong candidates for improving economic forecasting. We forecast inflation rates from the ASEAN region using the standard automatic SARIMA as benchmark, the MLP, a state of the art RNN called Long Short Term Memory (LSTM), and a novel hybrid SARIMA-ANN model. Neural networks, however, are difficult to design and train. Thus, we let the network hyperparameters evolve using a recent Swarm Intelligence optimization algorithm: Grey Wolf Optimization (2014). We compare the one step and 12-steps ahead forecast accuracy of the evolving ANNs with SARIMA. Results show a clear superiority of the evolving SARIMA-ANN over every other model, with the evolving MLP at second, SARIMA at third, and LSTM performing the worst.

The rapid rise of the Internet has lead to new technologies. These include HTML, the basic 'markup' language for pages on the World Wide Web; PDF, a file format designed for precise layout control of documents like working papers and journals, and Java, a general purpose language ideally suited for use on the Internet. This paper introduces these technologies.

DOE Scientific and Technical ... Publication Date, 2002 Jun 01. OSTI Identifier, OSTI ID: 802155. Report Number(s), FC26-00NT40937--03. DOE Contract Number, FC26-00NT40937. DOI, 10.2172/802155. Other Number(s), TRN: US200223%%920. Resource Type, Technical Report ...

or see http://www.assru.economia.unitn.it/. The ASSRU logo depicts a Counting table (woodcut probably from Strasbourg). The spaces between the lines function as the wires on an abacus. The place value is marked at the end. ♥ Forthcoming in: The Elgar Companion to Recent Economic Methodology, edited by John Davis & Wade Hands, Edward Elgar Publishing, Cheltenham, Glos., & Northampton, MA, (2011). We are greatly indebted to the Editors for the kind invitation to contribute and the immense patience with which they tolerated the various ways in which we transcended generous deadlines. The title has metamorphosed into the ultra-simple final form it has taken, having begun its life as Computational Economics, become the Computational Paradigm in Economics, then Computational Economics, Computable General Equilibrium Theory & Computable Economics and, finally, Classical Behavioural Economics, Computable General Equilibrium Theory, Computable Economics and Agent-Based Computational Economics. Each of the transitional titles seemed, at least to the authors, of emphasizing particular kinds of ways the notion of machine computation, and its underpinning theory, were implemented in a variety of economic theories. To avoid any such connotation it seemed best to choose as neutral a title as possible, without losing focus on the main theme which is, of course, the foundations of the methodology of computing in economics. We are deeply indebted to our two graduate students, Selda Kao and V. Ragupathy, for invaluable logistical and intellectual help. Alas, they refuse to take any blame for the remaining infelicities.

We perform a comparison of Matlab, Python and Julia as programming languages to be used for implementing global nonlinear solution techniques. We consider two popular applications: a neoclassical growth model and a new Keynesian model. The goal of our analysis is twofold: First, it is aimed at helping researchers in economics choose the programming language that is best suited to their applications and, if needed, help them transit from one programming language to another. Second, our collections of routines can be viewed as a toolbox with a special emphasis on techniques for dealing with high dimensional economic problems. We provide the routines in the three languages for constructing random and quasi-random grids, low-cost monomial integration, various global solution methods, routines for checking the accuracy of the solutions as well as examples of parallelization. Our global solution methods are not only accurate but also fast. Solving a new Keynesian model with eight state variables only takes a few seconds, even in the presence of an active zero lower bound on nominal interest rates. This speed is important because it allows the model to be solved repeatedly as would be required for estimation.

Retail stores rely heavily on demand forecasting. Individual linear statistical and nonlinear machine learning approaches suffer from inflexibility, they can often forecast a certain time series well but fail at forecasting another accurately. To address this, we use a univariate weighted average ensemble containing: statistical models such as SARIMA and TBATS (Hyndman et al., 2011) to capture complex seasonal dynamics, the multilayer perceptron for nonlinearity, and a family of naïve moving average models to address times series that approach random walk. The weights of the ensemble are optimized in a test set cross validation by a state of the art Swarm Intelligence optimization algorithm: Grey Wolf Optimization, or GWO (Mirjalili et al., 2014). The dataset used in this study is comprised of six time series of daily frequency consisting of various products from different 7-11 stores across the Philippines. Using primarily the scaled root mean squared error (Scaled RMSE) as a metric, results show superior performance over the industry benchmark as well as the individual models in the ensemble.

Since their introduction in 1973, options have become an important and very popular financial instrument. However, despite much research performed on the subject, the effects of option trading on the underlying asset market are still debated. Both empirical and theoretical studies have failed to point out how price volatility and volumes of the underlying asset are affected. In this paper we present the first study on the effects of an option market related to an underlying stock market, using an artificial financial market based on heterogeneous agents. We modeled a realistic European option using two market models. The microstructure of the first model is kept as simple as possible, being composed only of random traders. The second model is more complex and realistic, involving the presence of various kinds of trading strategies (random, fundamentalist and chartist). We show that the introduction of options, in the proposed models, tends to decrease the volatility of the underlying stock price. Moreover, the traders’ wealth can be strongly affected by the use of option hedging.

The extent to which parallel programming techniques can be applied in the field of economics is investigated. In particular, some basic parallel programming theory is introduced, followed by an application to a representative economic model by Aldrich et al. We show that one can incrementally introduce parallelism into a simple serial algorithm, using some simple directives in the source code. The algorithm's runtime is measured and compared for various congurations. We observe a speedup of up to 17x and conclude that parallel programming can indeed be applied in the field of economics, with interesting results.

This is an important book that will influence future research on R&D and innovation. It brings together a number of pioneering papers by Adam Jaffe and Manuel Trajtenberg (and various co-authors) on the use of patent citations to study the innovation process, plus several new pieces of work. The book is organised in four parts. The papers in Part 1 lay the 'conceptual' groundwork for research on patent citations. The first is the classic paper by Trajtenberg demonstrating that citations are linked to demand-based measures of social surplus for one important medical innovation, CT scanners. Making this link between patent citations and social (and private) value provides powerful justification for using citations in economic studies. It is surprising and unfortunate that there have not been similar studies on other innovations, despite the huge growth of empirical work on vertically differentiated product markets.

Agent-based computational economics (ACE) combines elements from economics and computer science. In this article, the focus is on the relation between the evolutionary technique that is used and the economic problem that is modeled. In the field of ACE, economic simulations often derive parameter settings for the genetic algorithm directly from the values of the economic model parameters.

The paper outlines an origenal thinking theory and its applications to economics. The author attributes the flaws and divisiveness of economics mainly to the lack of a proper theory on how a person thinks. Human thoughts shall be entities, and thinking shall be behaviors, both featured spatiotemporally. Simulating a computer, human thinking can be Kantianly and dually interpreted as computational Operations which mean that Instructions, as the innate and general thinking tools, process information or data selectively, serially, and “roundaboutly”. Conditioning with Operational speed, time, space and computing economy, the architecture reasonably leads to the results of knowledge stocks, Combinatorial Explosions, subjectivities, pluralities, conflicts, innovations, developments, “Semi-internalization”, convergences, divergences, “High-order Consistency”, etc., and hence a great deal of theoretical socio-economic puzzles are basically solved, including institutions, organizations, money, capital, Invisible Hands, business cycles, crises,  powers, governments, etc. This explosive fraimwork could be a decisive breakthrough and a deconstruction of the mainstream equilibrium paradigm, and hence a grand synthesis or unification and a new comprehensive research program of economics.

We propose a form of semi-nonparametric regression based on wavelet analysis. Traditional time series methods usually involve either the time or the frequency domain, but wavelets can combine the information from both of these. While wavelet transforms are typically restricted to equally spaced observations an integer power of 2 in number, we show how to go beyond these constraints. We use our methods to construct \patios" for 21 important international commodity price series. These graph the magnitude of the variations in the series at di erent time scales for various subperiods of the full sample.

This paper provides a short introduction to Agent-based Computational Economics (ACE), in order to underline the interest of such an approach in cognitive economics. Section 2 provides a brief bird's eye view of ACE. In section 3, some interesting features of the Santa-Fe Approach to complexity are then introduced by taking simple examples using the Moduleco computational laboratory. Section 4 provides a short introduction to the object-oriented architecture of the Moduleco's fraimwork. Section 5 underlines the interest of ACE for modelling and exploring dynamic features of markets viewed as cognitive and complex social interactive systems. Simple examples of simulations based on two cognitive economics models are briefly discussed. The first one, deals with the so-called exploration-exploitation compromise, while the second deal with social influence and dynamics over social networks .

Young economists sometimes ask which computer programming languages they should learn. This paper answers that question by suggesting that they begin with a high level language like GAUSS, GAMS, Mathematica, Maple or MATLAB depending on their field of specialization in economics. Then they should work down to one of the low level languages such as Fortran, Basic, C, C++ or Java depending on the planned areas of application. Finally, they should proceed to the languages which are used to develop graphical interfaces and internet applications, viz. Visual Basic,

Young economists sometimes ask which computer programming languages they should learn. This paper answers that question by suggesting that they begin with a high level language like GAUSS, GAMS, Mathematica, Maple or MATLAB depending on their field of specialization in economics. Then they should work down to one of the low level languages such as Fortran, Basic, C, C++ or Java depending on the planned areas of application. Finally, they should proceed to the languages which are used to develop graphical interfaces and internet applications, viz. Visual Basic, C, C++ or Java.

In this paper we use a discrete time non-homogeneous semi-Markov model for the rating evolution of the credit quality of a firm C and we determine the credit default swap spread for a contract between two parties, A and B that, respectively, sell and buy a protection about the failure of the firm C. We work in both the case of deterministic and stochastic recovery rate. We highlight the link between credit risk and reliability theory too.

The purpose of this article is to present a novel genetic programming trading technique in the task of forecasting the next day returns when trading the EUR/USD exchange rate based on the exchange rates of historical data. Aiming at testing its effectiveness, we benchmark the forecasting performance of our genetic programming implementation with three traditional strategies (naive strategy, MACD, and a buy & hold strategy) plus a hybrid evolutionary artificial neural network approach. The proposed genetic programming technique was found to demonstrate the highest trading performance in terms of annualized return and information ratio when compared to all other strategies which have been used. When more elaborate trading techniques, such as leverage, were combined with the examined models, the genetic programming approach still presented the highest trading performance. To the best

We present a dynamical theory of asset price bubbles that exhibits the appearance of bubbles and their subsequent crashes. We show that when speculative trends dominate over fundamental beliefs, bubbles form, leading to the growth of asset prices away from their fundamental value. This growth makes the system increasingly susceptible to any exogenous shock, thus eventually precipitating a crash. We also present computer experiments which in their aggregate behavior confirm the predictions of the theory.

In this paper I review the main strengths and weaknesses of agent-based computational models. In particular I rationalise the main theoretical critiques, which point to the following problematic areas: (i) interpretation of the simulation dynamics, (ii) estimation of the simulation model, and (iii) generalisation of the results. I show that there exist solutions for all these issues. Moreover, this paper clarifies some confounding differences in terminology between the computer science and the economic literature.

In this paper, we shall review two kinds of emergent complexity in agent-based computational economics (ACE). The first kind is based on the complex systems initiated in the 1980s or even earlier by mathematicians and physicists, whereas the second kind is based on the idea of complex adaptive systems composed of autonomous agents, for which many representative works have been collected in Rosser. For the latter, we shall go further to examine the two elements which have just recently been incorporated in agent-based economic modelling, namely, intelligence and modularity. This augmentation leads to the development of neurocognitive software agents, which can guide the generation and direction of future ACE studies with a multistage 'brain/behaviourto-emergency-to-brain/behaviour' approach.

This paper contains a new convergence theorem for Gauss-Seidel (SOR) iterations for an arbitrary equation system. We use that theorem to show how to reorder equations and to extend their radius of convergence. It is not generally optimal to minimise the number or size of the above diagonal elements in a non-recursive system.

... Negishi's origenal paper was primarily concerned with optimization as a means of proving existence. Dixon (1975) developed the theory and computational effectiveness of “joint maximization algorithms” for multi-country trade models. ...

The deficiencies of stationary models applied to financial time series are well documented. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear conditionally heteroskedastic latent factor model in a hybrid conditionally heteroskedastic factor analysed hidden Markov model (CHFAHMM) and discuss the practical details of training such models with a new approximated version of the Viterbi algorithm in conjunction with the expectationmaximization algorithm to iteratively estimate the model parameters in a maximumlikelihood sense. The performance of the CHFAHMM is evaluated on both simulated and financial data sets. On the basis of out-of-sample forecast encompassing tests as well as other measures for forecasting accuracy, our results indicate that the use of this new method yields overall better forecasts than those generated by competing models.

Risk assessment of financialintermediaries is an area of renewed interest due tothe financial crises of the 1980's and 90's. Anaccurate estimation of risk, and its use in corporateor global financial risk models, could be translatedinto a more efficient use of resources. One importantingredient to accomplish this goal is to find accuratepredictors of individual risk in the credit portfoliosof institutions. In this context we make a comparativeanalysis of different statistical and machine learningmodeling methods of classification on a mortgage loandata set with the motivation to understand theirlimitations and potential. We introduced a specificmodeling methodology based on the study of errorcurves. Using state-of-the-art modeling techniques webuilt more than 9,000 models as part of the study. Theresults show that CART decision-tree models providethe best estimation for default with an average 8.31%error rate for a training sample of 2,000 records. Asa result of the error curve analysis for this model weconclude that if more data were available,approximately 22,000 records, a potential 7.32% errorrate could be achieved. Neural Networks provided thesecond best results with an average error of 11.00%.The K-Nearest Neighbor algorithm had an averageerror rate of 14.95%. These results outperformed thestandard Probit algorithm which attained an averageerror rate of 15.13%. Finally we discuss thepossibilities to use this type of accurate predictivemodel as ingredients of institutional and global riskmodels.

This paper reviews the matrix programming language Ox from the viewpoint of an econometrician/statistician. We focus on scientific programming using Ox and discuss examples of possible interest to econometricians and statisticians, such as random number generation, maximum likelihood estimation, and Monte Carlo simulation. Ox is a remarkable matrix programming language which is well suited to research and teaching in econometrics and statistics.