Financial Optimization Models in Data Networks*

In a competitive market investors in a data network need to give utmost considerations on profitability. They must have clear picture of the size, growth rate and demand for different services. However, the investors’ budget may be limited, and therefore the speed at which the network is rolled out, must be carefully planned to ensure that they can meet profitability targets. We model first the roll out order as combinatorial optimization problems and then extend them as continuous optimization problems. We then implement these models in a practical problem. Numerical studies suggested that the optimization problems have multiple local minima. Therefore, a global optimization technique is used to obtain the global minimum for the continuous variable problem and a combinatorial optimization technique is used to solve the discrete variable problem. Optimal financial indicators are obtained to assess the commercial viability of the network. Finally, we demonstrate that the solution of these optimization problems can provide an investment policy to the investors in data networks. *This network is a combined telephone and data network such as VIP (Voice over Internet Protocol). M. M. Ali: Visitor at the Institute for Mathematics and its Applications, University of Minnesota, USA.     

Privatization and performance: evidence from telecommunications sector

There is a continuing debate on whether or not ownership changes accompanying privatization of state-owned enterprises (SOEs) lead to performance improvements of such firms. Since profitability measures alone are possibly inappropriate for SOEs, we address this very significant current question using a novel approach. We test the performance of a large sample of telecommunication firms around the world, 4 years before and 4 years after privatization, using two parallel measures namely financial performance measures and production performance measures. Our purpose is to identify if both approaches could corroborate stronger evidence for or against maintained hypothesis of performance improvements after privatization. The overall finding for this industry indicates significant improvements in both financial and production performance after privatization. Further research is warranted to extend this parallel-methods approach to firms in other industries.     

On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time à la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton–Jacobi–Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand.     

A modified Duckworth–Lewis method for adjusting targets in interrupted limited overs cricket

In this paper we present a modified Duckworth/Lewis method. The key modification is an improved functional form for the model describing the runs to be scored in an innings. In the course of our work we compare several alternative methods for resetting targets in limited overs cricket that have been proposed in the literature and conclude that the Duckworth/Lewis method is the most viable. Our analysis also suggests that it is reasonable to use a single method for both the 50-over and 20-over formats of the game.     

The impact of sample bias on consumer credit scoring performance and profitability

This article seeks to gain insight into the influence of sample bias in a consumer credit scoring model. In earlier research, sample bias has been suggested to pose a sizeable threat to predictive performance and profitability due to its implications on either population drainage or biased estimates. Contrary to previous—mainly theoretical—research on sample bias, the unique features of the data set used in this study provide the opportunity to investigate the issue in an empirical setting. Based on the data of a mail-order company offering short-term consumer credit to their consumers, we show that (i) given a certain sample size, sample bias has a significant effect on consumer credit-scoring performance and profitability, (ii) its effect is composed of the inclusion of rejected orders in the scoring model, and—to a lesser extent—the inclusion of these orders into the variable-selection process, and (iii) the impact of the effect of sample bias on consumer credit-scoring performance and profitability is modest.     

Modeling and analysis of the multiperiod effects of social relationship on supply chain networks

In this paper, we analyze the effects of levels of social relationship on a multiperiod supply chain network with multiple decision-makers (suppliers, manufacturers, and retailers) associated at different tiers. The model incorporates the individual attitudes towards disruption and opportunism risks and allows us to investigate the interplay of the heterogeneous decision-makers and to compute the resultant network equilibrium pattern of production, transactions, prices, and levels of social relationship over the multiperiod planning horizon. In our analysis, we focus on the following questions: (1) how do the evolving relationships affect the profitability and risks of supply chain firms as well as the prices and demands of the product in the market? (2) how do the relationships with the upstream supply chain firms affect the relationships with the downstream firms, and how these relationships influence the profitability and risks of the supply chain firms? (3) how do the supply disruption risks interact with the opportunism risks through supply chain relationships, and how these risks influence the profitability of the firms? The results show that high levels of relationship can lead to lower supply chain overall cost, lower risk, lower prices, higher product transaction and therefore higher profit.     

基于泰尔指数的盈利能力差异性测度研究

盈利能力是商业银行稳健性的重要保证。资产收益率(ROA)是衡量商业银行盈利能力的一个重要指标,但其无法直接衡量不同类型银行间盈利能力的差异性,也无法直接体现盈利能力差异不同影响因素的贡献度。基于此,本文的主要工作是在资产收益率的基础上,利用泰尔指数构造了单位资产收益率泰尔指数(ROUAT)与人均收益率泰尔指数(ROPPT)两个指标,用来测度商业银行盈利能力的差异性,并对中国13家上市商业银行2006~2015年的财务数据进行实证。实证结果表明:国有控股银行盈利能力的组内差异远大于股份制银行的组内差异,也大于国有控股银行和股份制银行的组间差异。通过对单位资产收益率泰尔指数(ROUAT)与人均收益率泰尔指数(ROPPT)对比,进一步发现人均收益率差异比单位资产收益率差异表现更为突出,说明现阶段银行的员工人数比银行的总资产对银行盈利能力的影响大。本文的主要贡献是利用泰尔指数和资产收益率构造了单位资产收益率泰尔指数和人均收益率泰尔指数两个指标,解决了不同分组下的商业银行的盈利能力差异性的测度问题,解决了差异性影响因素的贡献度问题,盈利能力差异性的测度为相关部门的政策制定提供参考。     

A Dynamic Analysis of Schelling’s Binary Corruption Model: A Competitive Equilibrium Approach

Schelling (in Micromotives and Macrobehavior, Norton, New York, 1978) suggested a simple binary choice model to explain the variation of corruption levels across societies. His basic idea was that the expected profitability of engaging in corruption depends on its prevalence. The key result of the so-called Schelling diagram is the existence of multiple equilibria and a tipping point. The present paper puts Schelling’s essentially static approach into an intertemporal setting. We show how the existence of an unstable interior steady state leads to thresholds such that history alone or history in addition to expectations (or coordination) is necessary to determine the long-run outcome. In contrast to the related literature, which classifies these two cases according to whether the unstable equilibrium is a node or a focus, the actual differentiation is more subtle because even a node can lead to an overlap of solution paths such that the initial conditions alone are insufficient to uniquely determine the competitive equilibrium. Another insight is that a (transiently) cycling competitive equilibrium can dominate the direct and monotonic route to a steady state, even if the direct route is feasible.     

No such thing as a perfect hammer: comparing different objective function specifications for optimal control

Linear-quadratic (LQ) optimization is a fairly standard technique in the optimal control framework. LQ is very well researched, and there are many extensions for more sophisticated scenarios like nonlinear models. Conventionally, the quadratic objective function is taken as a prerequisite for calculating derivative-based solutions of optimal control problems. However, it is not clear whether this framework is as universal as it is considered to be. In particular, we address the question whether the objective function specification and the corresponding penalties applied are well suited in case of a large exogenous shock an economy can experience because of, e.g., the European debt crisis. While one can still efficiently minimize quadratic deviations around policy targets, the economy itself has to go through a period of turbulence with economic indicators, such as unemployment, inflation or public debt, changing considerably over time. We test four alternative designs of the objective function: a least median of squares based approach, absolute deviations, cubic and quartic objective functions. The analysis is performed based on a small-scale model of the Austrian economy and illustrates a certain trade-off between quickly finding an optimal solution using the LQ technique (reaching defined policy targets) and accounting for alternative objectives, such as limiting volatility in economic performance. As an implication, we argue in favor of the considerably more flexible optimization technique based on heuristic methods (such as Differential Evolution), which allows one to minimize various loss function specifications, but also takes additional constraints into account.

     

Detecting Students' Experiences of Discontinuities Between Middle School and High School Mathematics Programs: Learning During Boundary Crossing

Transitions from middle school to high school mathematics programs can be problematic for students due to potential differences between instructional approaches and curriculum materials. Given the minimal research on how students experience such differences, we report on the experiences of two students as they moved out of an integrated, problem-based mathematics program in their middle school into a high school mathematics program that emphasized procedural fluency. We conducted an average of two interviews per year for two and a half years with participants and engaged in participant-observation at their high school. In this study, we illustrate an analytic process for detecting discontinuities between settings from participants' perspectives. We determined that students experienced a discontinuity if they reported meaningful differences between settings (frequent mention, in detail, with emphasis terms) and concurrently reported a change in attitude. Additionally, these students' experiences illustrate two opportunities to learn during boundary-crossing experiences: identification and reflection.     

Approximate Bayesian Computation and Model Assessment for Repulsive Spatial Point Processes

In many applications involving spatial point patterns, we find evidence of inhibition or repulsion. The most commonly used class of models for such settings are the Gibbs point processes. A recent alternative, at least to the statistical community, is the determinantal point process. Here, we examine model fitting and inference for both of these classes of processes in a Bayesian framework. While usual MCMC model fitting can be available, the algorithms are complex and are not always well behaved. We propose using approximate Bayesian computation (ABC) for such fitting. This approach becomes attractive because, though likelihoods are very challenging to work with for these processes, generation of realizations given parameter values is relatively straightforward. As a result, the ABC fitting approach is well-suited for these models. In addition, such simulation makes them well-suited for posterior predictive inference as well as for model assessment. We provide details for all of the above along with some simulation investigation and an illustrative analysis of a point pattern of tree data exhibiting repulsion. R code and datasets are included in the supplementary material.     

基于风险调整资本收益率下的最优再保险策略

风险调整资本收益率是一个用来描述赚取收益所承担风险的重要指标,是衡量风险调整后的财务绩效的一个有效工具,在银行业中得到广泛采用。近年来,在保险公司的再保险业务中,也越来越多地采用风险调整资本收益率这一指标来衡量收益和风险。本文重新考虑了有再保险控制下的风险调整资本收益率,并得到:在一般再保险自留函数下,我们证明了分层再保险策略是最优再保险形式;进一步,我们获得了最优再保险分层水平及最优风险调整资本收益率;最后,我们也给出了算例及数值分析。     

The informational content of insider trading disclosures: empirical results for the Polish stock market

In this paper, we try to answer the question as to whether insider trading disclosures convey valuable information to market participants, valuable in the sense of the profitability of an investment strategy that faithfully mirrors insider behaviour. Our interest in this subject is limited to the case of announcements concerning insider transactions issued over a 6 year-period on the Warsaw Stock Exchange (WSE). Initially, we use event study methodology to check whether insider trading disclosures are accompanied by a performance of stock returns as well as trading volume. Two different models generating expected returns (expected volume) are employed to verify the robustness of our results. The first of these is the regime switching model, with the results then being recalculated by using a GARCH-type model which seem to be most useful for dealing with some of the inconvenient statistical properties of stock return and trading volume data. Afterwards, a technique based on the reference return strategies is used to examine whether or not outsiders who imitate insider behaviour are able to profit from it. The major findings are as follows: firstly, announcements about the sale of stocks by insiders convey no information to market participants. Secondly, a statistically significant market response to insider disclosures of purchases of stocks in their own company can be observed in the three days prior to the announcement release for both return as well as trading volume series, and finally, outsiders who purchased stocks previously bought by insiders experience negative returns whereas outsiders disposing of stocks previously sold by insiders earned a return of 8.57% over the 6 month-period.      

The effects of asset specificity on maintenance financial performance: An empirical application of Transaction Cost Theory to the medical device maintenance field

This study uses multivariate regression analysis to examine the effects of asset specificity on the financial performance of both external and internal governance structures for medical device maintenance, and investigates how the financial performance of external governance structures differs depending on whether a hospital is private or public. The hypotheses were tested using information on 764 medical devices and 62 maintenance service providers, resulting in 1403 maintenance transactions. As such, our data sample is significantly larger than those used in previous studies in this area. The results empirically support our core theoretical argument that governance financial performance is influenced by assets specificity.     

Supply chain coordination for the joint determination of order quantity and reorder point using credit option

Decisions regarding order quantity and reorder point are two major challenges in supply chain inventory management. In this paper, a coordination model of the joint determination of these two decision variables is proposed. A decentralized supply chain consisting of one buyer and one supplier in a multi-period setting is investigated. Demand and lead times are uncertain in our model. An incentive scheme based on credit option has been developed to encourage the buyer to participate in the coordination model. In this model, the downstream member has the option of using credit to purchase goods during the credit time, subject to its commitment to a jointly agreed order quantity and reorder point. The credit time is determined in such a way that the two parties have incentives to participate. The proposed incentive scheme can share the benefits of coordination between the two members based on their bargaining power. The proposed model shows that the coordination of the reorder point, together with order quantity, can increase the overall chain profitability as well as each member’s profitability.     

Prediction of financial distress: An empirical study of listed Chinese companies using data mining

The deterioration in profitability of listed companies not only threatens the interests of the enterprise and internal staff, but also makes investors face significant financial loss. It is important to establish an effective early warning system for prediction of financial crisis for better corporate governance. This paper studies the phenomenon of financial distress for 107 Chinese companies that received the label ‘special treatment’ from 2001 to 2008 by the Shanghai Stock Exchange and the Shenzhen Stock Exchange. We use data mining techniques to build financial distress warning models based on 31 financial indicators and three different time windows by comparing these 107 firms to a control group of firms. We observe that the performance of neural networks is more accurate than other classifiers, such as decision trees and support vector machines, as well as an ensemble of multiple classifiers combined using majority voting. An important contribution of the paper is to discover that financial indicators, such as net profit margin of total assets, return on total assets, earnings per share, and cash flow per share, play an important role in prediction of deterioration in profitability. This paper provides a suitable method for prediction of financial distress for listed companies in China.     

A primal-dual approximation algorithm for a two depot heterogeneous traveling salesman problem

Surveillance applications require a collection of heterogeneous vehicles to visit a set of targets. We consider a fundamental routing problem that arises in these applications involving two vehicles. Specifically, we consider a routing problem where there are two heterogeneous vehicles that start from distinct initial locations and a set of targets. The objective is to find a tour for each vehicle such that each of the targets is visited at least once by a vehicle and the sum of the distances traveled by the vehicles is minimal. We consider an important special case of this routing problem where the travel costs satisfy the triangle inequality and the following monotonicity property: the first vehicle’s cost of traveling between any two targets is at most equal to the second vehicle’s cost of traveling between the same targets. We present a primal-dual algorithm for this case that provides an approximation ratio of 2.     

Credit card pricing and impact of adverse selection

Variable pricing is one way of improving the profitability of credit cards when the price is the interest rate to be charged. However, choosing the appropriate price for each risk grade of default is not straightforward, as one of the main problems is adverse selection, when the lender finds that the borrowers who actually take a specific offer have a higher default rate than expected. We show that modelling the choice of credit card by the borrower as an auction process means that the winner's curse can lead to adverse selection. By modelling the way lenders use the credit score of a borrower in their pricing decision we are able to show that there is a simple relationship between the actual probability of a borrower repaying and what the successful lender believes this probability to be, regardless of the distribution of the errors caused by adverse selection. This allows one to assess the impact on profitability of these errors.     

Developing a decomposable measure of profit efficiency using DEA

In for-profit organizations efficiency measurement with reference to the potential for profit augmentation is particularly important as is its decomposition into technical, and allocative components. Different profit efficiency approaches can be found in the literature to measure and decompose overall profit efficiency. In this paper, we highlight some problems within existing approaches and propose a new measure of profit efficiency based on a geometric mean of input/output adjustments needed for maximizing profits. Overall profit efficiency is calculated through this efficiency measure and is decomposed into its technical and allocative components. Technical efficiency is calculated based on a non-oriented geometric distance function (GDF) that is able to incorporate all the sources of inefficiency, while allocative efficiency is retrieved residually. We also define a measure of profitability efficiency which complements profit efficiency in that it makes it possible to retrieve the scale efficiency of a unit as a component of its profitability efficiency. In addition, the measure of profitability efficiency allows for a dual profitability interpretation of the GDF measure of technical efficiency. The concepts introduced in the paper are illustrated using a numerical example.     

Best Fourier Approximation and Application in Efficient Blurred Signal Reconstruction

We expand upon the known results on sharp linear Fourier methods of approximation where the approximation is the best in terms of both rate and constant among all polynomial procedures of approximation. So far these results have been studied due to their mathematical beauty rather than their practical importance. In this paper we show that they are the core mathematics underlying best statistical methods of solving noisy ill-posed problems. In particular, we suggest a procedure for recovery of noisy blurred signals based on samples of small sizes where a traditional statistics concludes that the complexity of such a setting makes the problem not worthy of a further study. Thus, we present a problem where a combination of the classical approximation theory and statistics leads to interesting practical results.