Entropy and algorithmic complexity in quantum information theory

A theorem of Brudno says that the entropy production of classical ergodic information sources equals the algorithmic complexity per symbol of almost every sequence emitted by such sources. The recent advances in the theory and technology of quantum information raise the question whether a same relation may hold for ergodic quantum sources. In this paper, we discuss a quantum generalization of Brudno’s result which connects the von Neumann entropy rate and a recently proposed quantum algorithmic complexity.     

The role of algorithmic trading systems on stock market efficiency

The rapid development of information technology has changed the dynamics of financial markets. The main purpose of this study is laid on examining the role of IT based stock trading on financial market efficiency. This research specifically focused on algorithmic trading. Algorithmic trading enables investors to trade stocks through a computer program without the need for human interventions. Based on an empirical analysis of the Korean stock market, this study discovered the positive impact of algorithmic trading on stock market efficiency at three-fold. First, the study results indicate that algorithmic trading contributes to the reduction in asymmetric volatility, which causes inefficiency of information in a stock market. Second, an algorithmic trading also increases the operation efficiency of a stock market. Arbitrage trading contributes on the equilibrium between the spot market and futures market as well as on the price discovery. Third, algorithmic trading provides liquidity for market participants contributing to friction free transactions. The research results indicate that stock exchanges based on electronic communications networks (ECNs) without human intervention could augment a financial market quality by increasing trading share volumes and market efficiency so that it can eventually contribute to the welfare of market investors.     

On the algorithmic complexity of associative algebras

The complexity L(A) of a finite dimensional associative algebra A is the number of non-scalar multiplications/divisions of an optimal algorithm to compute the product of two elements of the algebra. We show

$\text{L(A) ? 2ddim A?t}$

, where t is the number of maximal two-sided ideals of A.     

The algorithmic complexity of mixed domination in graphs

Let G=(V,E) be a simple graph with vertex set V and edge set E. A subset W⊆V∪E is a mixed dominating set if every element x∈(V∪E)?W is either adjacent or incident to an element of W. The mixed domination problem is to find a minimum mixed dominating set of G. In this paper we first prove that a connected graph is a tree if and only if its total graph is strongly chordal, and thus we obtain a polynomial-time algorithm for this problem in trees. Further we design another linear-time labeling algorithm for this problem in trees. At the end of the paper, we show that the mixed domination problem is NP-complete even when restricted to split graphs, a subclass of chordal graphs.     

On the algorithmic complexity of the Mastermind game with black-peg results

In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show that it is NP-complete to determine if a sequence of single-color Mastermind results have a satisfying vector. We also show how to devise efficient algorithms for discovering a hidden vector through single-color queries. Indeed, our algorithm improves a previous method of Chvátal by almost a factor of 2.     

An intelligent market making strategy in algorithmic trading

Market making (MM) strategies have played an important role in the electronic stock market. However, the MM strategies without any forecasting power are not safe while trading. In this paper, we design and implement a twotier framework, which includes a trading signal generator based on a supervised learning approach and an event-driven MM strategy. The proposed generator incorporates the information within order book microstructure and market news to provide directional predictions. The MM strategy in the second tier trades on the signals and prevents itself from profit loss led by market trending. Using half a year price tick data from Tokyo Stock Exchange (TSE) and Shanghai Stock Exchange (SSE), and corresponding Thomson Reuters news of the same time period, we conduct the back-testing and simulation on an industrial near-to-reality simulator. From the empirical results, we find that 1) strategies with signals perform better than strategies without any signal in terms of average daily profit and loss (PnL) and sharpe ratio (SR), and 2) correct predictions do help MM strategies readjust their quoting along with market trending, which avoids the strategies triggering stop loss procedure that further realizes the paper loss.     

Determining of stock investments with grey relational analysis

Selecting stock is important problem for investors. Investors can use related financial ratios in stock selection. These kind of worthy financial ratios can be obtained from financial statements. The investors can use these ratios as criteria while they are selecting the stocks. Since dealing with more than one financial ratio, the investing issue becomes multi-criteria decision making (MCDM) problem for the investors. There are various techniques for solving MCDM problems in literature. In this study grey relational analysis (GRA) is used for ordering some financial firms’ stocks which are in Financial Sector Index of Istanbul Stock Exchange (ISE). Besides, because of the importance of criteria weights in decision making, three different approaches – heuristic, Analytic Hierarchy Process, learning via sample – were experimented to find best values of criteria weights in GRA process.     

Expected benefits of information security investments

Ideally, decisions concerning investments of scarce resources in new or additional procedures and technologies that are expected to enhance information security will be informed by quantitative analyses. But security is notoriously hard to quantify, since absence of activity challenges us to establish whether lack of successful attacks is the result of good security or merely due to good luck. However, viewing security as the inverse of risk enables us to use computations of expected loss to develop a quantitative approach to measuring gains in security by measuring decreases in risk. In using such an approach, making decisions concerning investments in information security requires calculation of net benefits expected to result from the investment. Unfortunately, little data are available upon which to base an estimate of the probabilities required for developing the expected losses. This paper develops a mathematical approach to risk management based on Kaplan–Meier and Nelson–Aalen non-parametric estimators of the probability distributions needed for using the resulting quantitative risk management tools. Differences between the integrals of these estimators evaluated for enhanced and control groups of systems in an information infrastructure provide a metric for measuring increased security. When combined with an appropriate value function, the expected losses can be calculated and investments evaluated quantitatively in terms of actual enhancements to security.     

Predictive complexity and information

The notions of predictive complexity and of corresponding amount of information are considered. Predictive complexity is a generalization of Kolmogorov complexity which bounds the ability of any algorithm to predict elements of a sequence of outcomes. We consider predictive complexity for a wide class of bounded loss functions which are generalizations of square-loss function. Relations between unconditional KG(x) and conditional KG(x|y) predictive complexities are studied. We define an algorithm which has some “expanding property”. It transforms with positive probability sequences of given predictive complexity into sequences of essentially bigger predictive complexity. A concept of amount of predictive information IG(y:x) is studied. We show that this information is noncommutative in a very strong sense and present asymptotic relations between values IG(y:x), IG(x:y), KG(x) and KG(y).     

Interorganizational information sharing in the airline industry: An analysis of stock market responses to code-sharing agreements

This paper addresses the issue of inter-organizational information sharing alliances and their impacts on firm values from the perspective of inter-organizational coordination between partners in the airline industry setting. We investigate the shareholder wealth effects of inter-organizational information-sharing alliance arrangements, using 131 code-sharing agreements in the airline industry during 1984–1997. Employing event study methodology we found that the information sharing alliances between similar partners did create positive value in terms of stock returns at the time of alliance announcements to major US airlines. However, alliances between dissimilar partners resulted in significant losses of shareholder value to the major airlines. These results strongly support our main hypotheses that information-sharing alliances are successful and the benefits of such alliances are realized only when the coordination difficulties can be effectively dealt with.     

Profit-maximizing firm investments in customer information security

When a customer interacts with a firm, extensive personal information often is gathered without the individual's knowledge. Significant risks are associated with handling this kind of information. Providing protection may reduce the risk of the loss and misuse of private information, but it imposes some costs on both the firm and its customers. Nevertheless, customer information security breaches still may occur. They have several distinguishing characteristics: (1) typically it is hard to quantify monetary damages related to them; (2) customer information security breaches may be caused by intentional attacks, as well as through unintentional organizational and customer behaviors; and (3) the frequency of such incidents typically is low, although they can be very costly when they occur. As a result, predictive models and explanatory statistical analysis using historical data have not been effective. We present a profit optimization model for customer information security investments. Our approach is based on value-at-risk methods and operational risk modeling from financial economics. The main results of this work are that we: (1) provide guidance on the trade-offs between risk and return in customer information security investments; (2) define the range of efficient investments in technology-supported risk indemnification for sellers; (3) model how to handle government-dictated levels of investment versus self-regulation of investments in technology; and (4) characterize customer information security investment levels when the firm is able to pass some of its costs on to consumers. We illustrate our theoretical findings with empirical data from the Open Security Foundation, as a means of grounding our analysis and offering the reader intuition for the managerial interpretation of our theory and main results. The results show that we can narrow the decision set for solution providers and policy-makers based on the estimable risks and losses associated with customer information security. We also discuss the application of our approach in practice.     

The effect of investor psychology on the complexity of stock market: An analysis based on cellular automaton model

In this paper, using a developed cellular automaton model of the stock market, variables reflecting fractal and stability properties are introduced to describe complexity in the stock market; the concept of discrete level is defined to characterize market stability. Based on the model, the dependency of market complexity on the investors’ imitation degree is investigated. The results show a clear correlation between investors’ imitation degree and complexity of the stock market.     

Bifurcations in a stock market model

A theoretical framework is laid out, where a Stock Exchange is represented as a process under decentralized control. Attention is devoted to a specific case, in which the trading activity is described by a second order dynamical system. Three economically significant modes of behavior are identified. The stock market can (1)_adjust to a stable equilibrium, (2) approach a stable limit cycle, (3) diverge to infinity. The transition from mode (1) to mode (2) is a supercritical Hopf bifurcation, whereas the transition from mode (2) to mode (3) is a homoclinic bifurcation.     

A complexity analysis and an algorithmic approach to student sectioning in existing timetables

We show that the following fundamental question in student sectioning can be efficiently decided in polynomial time: Is it possible to assign \(m\) students to \(k\) sectioned courses with respect to a given timetable with \(l\) timeslots such that the individual capacities of all sections are not exceeded and no student has more than one appointment per timeslot? Our result opens the possibility of efficiently checking the feasibility of candidate timetables with respect to this question as part of timetabling algorithms. Based on a succinct representation of solutions, we also provide an algorithm to compute optimal assignments in \(O( k^2l^2 \log (\mathrm{sum}_{A}))\), where \(\mathrm{sum}_{A}\) is the sum of all specified section capacities. On the other hand, we prove that adding any single of the following constraints turns the above question into an NP-complete problem:

• Course-selection constraint: Student’s course-selections must be respected.
• Timeslot constraint: Students have individual timeslot restrictions.
• Multiple-event constraint: Sections may have multiple events in the timetable, and there must be no timeslot clashes between all section-events for each student.

Hence our investigation gives insight into the location of the borderline between efficiently solvable and computationally hard problem variations.

     

Mining the co-movement in the Taiwan stock funds market

Mutual funds are an essential tool for investors looking to diversify their investments. Facing various mutual funds, it is necessary to evaluate their performances. This study uses association rules to understand the relationships among various mutual funds. First, equity funds are categorized into high, medium and low risk levels. This study then evaluates the co-movement among funds within the same risk level and among funds across different risk levels. This study concludes that within any given risk level, the performances of at least seven funds exhibit strong co-movement. This study also shows the influence of the global economy on the correlations among different funds. Finally, investment recommendations are provided based on the findings.     

Finding trading patterns in stock market data

This article describes our design and evaluation of a multisensory human perceptual tool for the real-world task domain of stock market trading. The tool is complementary in that it displays different information to different senses - our design incorporates both a 3D visual and a 2D sound display. The results of evaluating the tool in a formal experiment are complex. The data mined in this case study is bid-and-ask data - also called depth-of-market data - from the Australian Stock Exchange. Our visual-auditory display is the bid-ask-land-scape, which we developed over much iteration with the close collaboration of an expert in the stock market domain. From this domain's perspective, the project's principal goal was to develop a tool to help traders uncover new trading patterns in depth-of-market data. In this article, we not only describe the design of the bid-ask-landscape but also report on a formal evaluation of this visual-auditory display. We tested nonexperts on their ability to use the tool to predict the future direction of stock prices.     

Predicting published news effect in the Brazilian stock market

The Efficient Market Hypothesis states that the value of an asset is given by all information available in the present moment. However, there is no possibility that a single financial analyst be aware of all published news which refers to a collection of stocks in the moment they are published. Thus, a computer system that applies text mining techniques and the GARCH model for predicting the volatility of financial assets may helps analysts and simple investors classifying automatically the news which cause the higher impact on stock market behavior. This work has the goal of creating a method for analyzing Portuguese written news’s content about companies that have their stocks negotiated in a stock market and trying to predict what kind of effect these news will cause in the Brazilian stock market behavior. Also, it was demonstrated in this study that it is possible to find out whether certain news may cause a considerable impact on prices of a negotiated stock.