Volume 25, Issue 2 (2014), pp. 241–264
The optimal financial investment (Portfolio) problem was investigated by leading financial organizations and scientists. Nobel prizes were awarded for the Modern Portfolio Theory (MPT) and further developments. The aim of these works was to define the optimal diversification of the assets depending on the acceptable risk level.
In contrast, the objective of this work is to provide a flexible, easily adaptable model of virtual financial markets designed for the needs of individual users in the context of utility theory. The aim is to optimize investment strategies. This aim is the new element of the proposed model and simulation system since optimization is performed in the space of investment strategies; both short term and longer term.
The new and unexpected result of experiments with the historical financial time series using the PORTFOLIO model is the observation that the minimal prediction errors do not provide the maximal profits.
Volume 23, Issue 3 (2012), pp. 405–425
The paper deals with the problem of high-school time-tabling that is important in applications, but hard for solving. The algorithm is presented for timetabling based on Multi-start and Simulated Annealing with parameters adapted using the Bayes approach. The algorithm proposed is compared with other timetabling algorithms using the web-based software. A multi-start algorithm is a simple way to provide the convergence, if the number of uniformly distributed starting points is large. A disadvantage is slow convergence.
Therefore, the first aim of this paper is experimental comparisons of the efficiency of different versions of multi-start algorithms in the optimization of timetables. To obtain representative results, the algorithms should be compatible with the Lithuanian high school practice and flexible enough for adaptation to different high schools.
The second aim is a web-based implementation of these algorithms in a way convenient for high schools. The web-based software is important for evaluation and comparison of algorithms by independent experts, as well, since the efficiency of algorithms depends on subjective parameters specific to each school, so on-line calculations are needed to obtain representative data. It is useful for scientific cooperation and applications to different schools. In addition, the software for evaluating of real timetables is included to compare with the results of optimization.
Volume 23, Issue 1 (2012), pp. 77–104
A simple Stock Exchange Game Model (SEGM) was introduced in Mockus (2003), to simulate the behavior of several stockholders using fixed buying-selling margins at fixed bank yield.
In this paper, an extended model USEGM is proposed. The advantage of USEGM is application of the Nash Equilibrium (NE) to strategies that define buying-selling margins and bank haircuts dynamically. This enables us to simulate market illiquidity that is an important feature of the present financial crisis (Allen, 2008). In addition, USEGM includes the transaction costs to reflect the reality better. To represent users that prefer linear utility functions, USEGM adds the AR-ABS(p) autoregressive model, minimizing the absolute values, to the traditional AR(p) model minimizing least square deviations.
A formal application of NE to simulate the behavior of market participants is a new feature of these models. In the well-known works Allen (2008), Brunnermeier (2009), Brunnermeier and Yogo (2009) equilibrium ideas were applied to supply-demand balance concepts, as usual.
The objective of USEGM is not forecasting, but simulation of financial time series that are affected by predictions of the participants. The “ virtual” stock exchange can help in testing the assumption of rational investor behavior vs the recent theories that explain financial markets by irrational responses of major market participants (Krugman, 2000, 2008, 2009). The model helps comparing expected profits of different prediction models using the virtual and historical data.
The model has been compared with eighteen actual financial time series and found the results to be close in many cases.
Volume 22, Issue 4 (2011), pp. 521–536
A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown.
To address that, we propose a novel method called Pareto–Lipschitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitz constants. In the proposed approach, a set of all unknown Lipschitz constants is regarded as multiple criteria using the concept of Pareto Optimality (PO).
We compare PLO to the existing algorithm DIRECT. We show that, in contrast to PLO, the DIRECT algorithm considers only a subset of PO decisions that are selected by a heuristic rule depending on an adjustable parameter. It means that some PO decisions are preferred to others. By contrast, PLO regards all PO decisions without preferences and is naturally suited to utilize highly parallel computing.
Volume 20, Issue 1 (2009), pp. 79–98
The objective of this paper is the description, justification, and web-based implementation of polynomial time algorithms for equilibrium search of Quadratic Bimatrix Games (QBG). An algorithm is proposed combining exact and heuristic parts. The exact part has the Irelevant Fraud (IF) component for cases when an equilibrium exists with no pure strategies. The Direct Search (DS) component finds a solution if an equilibrium exists in pure strategies. The heuristic Quadratic Strategy Elimination (QSE) part applies IF and DS to reduced matrices obtained by sequential elimination of strategies that lead to non-positive IF solutions. Finally, penalties needed to prevent unauthorized deals are calculated based on Nash axioms of two-person bargaining theory. In the numeric experiments QSE provided correct solution in all examples. The novel results include necessary and sufficient conditions when the QBG problem is solved by IF algorithm, the development of software and the experimental testing of large scale QBG problems up to n=800. The web-site http://pilis.if.ktu.lt/~jmockus includes this and accompanying optimization models.
Volume 19, Issue 1 (2008), pp. 45–62
The aim is to investigate two emerging information technologies in graduate studies and scientific cooperation. Internet is the first technology. The open source is the second. They help each other in many ways. The joint influence of both is regarded in this paper.
Results of complexity theory show the limitations of exact analysis. That explains popularity of heuristic algorithms. It is well known that efficiency of heuristics depends on the parameters. Therefore automatic procedures for tuning the heuristics help to compare results of different heuristics and enhance their efficiency.
The theory and some applications of Bayesian Approach were discussed in (Mockus, 2006a). In this paper examples of Bayesian Approach to automated tuning of heuristics are investigated. This is the Bayesian Heuristic Approach, in short. The examples of traditional methods of optimization, including applications of linear and dynamic programming, will be investigated in the next paper. These three papers represents three parts of the same work. However each part can be read independently.
All the algorithms are implemented as platform independent Java applets or servlets. Readers can easily verify and apply the results for studies and for real life optimization problems.
The theoretical result is application of unified Bayesian Heuristic Approach for different discrete optimization models. The practical result is adaptation of these models for graduate distance studies and scientific collaboration by a common java global optimization framework.
The software is regularly updated and corrected responding to new programming tools and users reports. However the general structure of web sites remains. The information is on the web site: http://pilis.if.ktu.lt/~mockus and four mirror sites.
Volume 17, Issue 2 (2006), pp. 259–278
The objective is to investigate two emerging information technologies in graduate studies and scientific cooperation. Internet is the first technology. The open source is the second. They help each other in many ways. We investigate the joint influence of both.
Results of complexity theory show the limitations of exact analysis. That explains popularity of heuristic algorithms. It is well known that efficiency of heuristics depends on the parameters. Thus we need some automatic procedures for tuning the heuristics. That helps comparing results of different heuristics. This enhance their efficiency, too.
An initial presentation of the basic ideas is in (Mockus, 2000). Preliminary results of distance graduate studies are in (Mockus, 2006a). Examples of optimization of sequential statistical decisions are in (Mockus, 2006b).
In this paper the theory and applications of Bayesian Heuristic Approach are discussed. In the next paper examples of Bayesian Approach to automated tuning of heuristics will be regarded. The examples of traditional methods of optimization including applications of linear and dynamic programming will be investigated in the last paper. These papers represents three parts of the same work. However each part can be read independently.
All the algorithms are implemented as platform independent Java applets or servlets. Readers can easily verify and apply the results for studies and for real life optimization models.
The information is on the main web-site http://pilis.if.ktu.lt/∼jmockus and four mirrors.
Volume 15, Issue 4 (2004), pp. 525–550
Walras theory is well known and widely used in models of market economy. Various iterative methods are developed to search for the equilibrium conditions.
In this paper a new approach is proposed and implemented where the search for Walras equilibrium is defined as a stochastic global optimization problem. This way random nature of customer arrivals is represented and the convergence to equilibrium is provided if equilibrium exists.
This paper describes a part of a Web‐based integrated system for scientific cooperation and distance graduate studies of theories of optimization, games and markets which aim is to provide researchers and graduate students with hands‐on experience on effective use of software. The objectives are to provide a tool for scientific collaboration and to stimulate creative abilities of graduate students to work as independent researchers. The web‐site http://soften.ktu.lt/˜mockus includes a family of economic and finnacial models regarding them all as examples of the the general optimization theory.
Volume 13, Issue 3 (2002), pp. 311–332
Real life scheduling problems are solved by heuristics with parameters defined by experts, as usual. In this paper a new approach is proposed where the parameters of various heuristics and their random mixtures are optimized to reduce the average deviations from the global optimum.
In many cases the average deviation is a stochastic and multi-modal function of heuristic parameters. Thus a stochastic global optimization is needed. The Bayesian heuristic approach is developed and applied for this optimization. That is main distinctive feature of this work. The approach is illustrated by flow-shop and school scheduling examples. Two versions of school scheduling models are developed for both traditional and profiled schools. The models are tested while designing schedules for some Lithuanian schools. Quality of traditional schedules is defined by the number of teacher “windows”. Schedules of profiled schools are evaluated by user defined penalty functions. That separates clearly subjective and objective data. This is the second specific feature of the proposed approach.
The software is developed for the Internet environment and is used as a tool for research collaboration and distance graduate studies. The software is available at web-sites and can be ran by standard net browsers supporting Java language. The care is taken that interested persons could easily test the results and apply the algorithms and software for their own problems.
Volume 10, Issue 2 (1999), pp. 231–244
In this paper two popular time series prediction methods – the Auto Regression Moving Average (ARMA) and the multilayer perceptron (MLP) – are compared while forecasting seven real world economical time series. It is shown that the prediction accuracy of both methods is poor in ill-structured problems. In the well-structured cases, when prediction accuracy is high, the MLP predicts better providing lower mean prediction error.