A partial adjustment valuation approach with stochastic and dynamic speeds of partial adjustment to measuring and evaluating the business value of information technology

This paper extends previous studies to develop a partial adjustment valuation (PAV) approach in which the speeds of partial adjustment are assumed to be stochastic and dynamic over time in measuring and evaluating the values of information technology and others (e.g., e-commerce or EC, brand name, etc.). A practical application is presented to demonstrate the application of the proposed PAV approach and it is compared to the other two existing PAV approaches.     

Adaptive expectations and dynamic adjustment in noncooperative games with incomplete information

This paper is concerned with the analysis of a Nash equilibrium of a noncooperative game. It can be shown that, without complete information about the other players' objectives or interests, the group of players, as a whole, can reach a Nash equilibrium by adopting a class of adaptive expectation and dynamic adjustment processes. It is shown that, if the expectation and adjustment processes are made continuously, the stability of the overall dynamic process is independent of the specific mechanisms of the expectation and the adjustment, but depends on the properties of each player's objective or payoff function. If, however, expectation and adjustment processes are made at discrete time intervals, the stability of the discrete process depends on the speed of adjustment chosen by each player.This research was supported by ONR Contract No. N00014-75-C-0738. The authors are indebted to the referee for several valuable comments and suggestions for improvement.     

风险投资估值调整协议的实物期权价值及其应用

为了分析风险投资估值调整协议的合理应用对于风险投资活动的重要意义.本文以蒙牛与大摩等投资机构签订的估值调整协议为现实背景,凝练出了估值调整协议的特点:规避风险、达到双赢是估值调整协议的目标;不确定性是估值调整协议的基础;绩效考核是约束手段、股权是激励筹码;合理估值是实现双赢的必备条件.基于上述特点,本文构建了估值调整协议的实物期权模型,证明给出估值调整协议的实物期权价值及双赢后风险投资主体退出的最佳时机解析解,并通过算例进行了验证,最后得出了风险投资估值调整协议是以双赢和规避风险作为其目标,并当项目价值大于约定临界值后,风险投资主体并不会长时间的等待而是及时选择合适时机退出的结论.     

Approximation of the steepest descent direction for the O-D matrix adjustment problem

In this paper, a method to approximate the directions of Clarke's generalized gradient of the upper level function for the demand adjustment problem on traffic networks is presented. Its consistency is analyzed in detail. The theoretical background on which this method relies is the known property of proximal subgradients of approximating subgradients of proximal bounded and lower semicountinuous functions using the Moreau envelopes. A double penalty approach is employed to approximate the proximal subgradients provided by these envelopes. An algorithm based on partial linearization is used to solve the resulting nonconvex problem that approximates the Moreau envelopes, and a method to verify the accuracy of the approximation to the steepest descent direction at points of differentiability is developed, so it may be used as a suitable stopping criterion. Finally, a set of experiments with test problems are presented, illustrating the approximation of the solutions to a steepest descent direction evaluated numerically. Research supported under Spanish CICYT project TRA99-1156-C02-02.     

The speed of adjustment of financial ratios: A hierarchical Bayesian approach using mixtures

This paper presents a hierarchical Bayesian analysis of the partial adjustment model of financial ratios using mixture models, an approach that allows us to estimate the distribution of the adjustment coefficients. More particularly, it enables us to analyse speed of reaction in the presence of shocks affecting financial ratios objectives as a basis to establish homogenous groups of firms. The proposed methodology is illustrated by examining a set of ratios for a sample of firms operating in the U.S. manufacturing sector. Copyright © 2007 John Wiley & Sons, Ltd.     

The persistence of abnormal return on assets: an exploratory analysis of the performance of firms by country and sector

This study offers an exploratory statistical analysis of the persistence of annual abnormal returns across a sample of firms from different European Union countries. To this end, a hierarchical Bayesian dynamic model has been used that enables the annual behaviour of those profits to be broken down into a permanent structural component and a transitory component, while also distinguishing between general effects affecting the industry as a whole and specific effects impacting on each firm in particular. This breakdown of the behaviour of profits allows for a more accurate assessment of the relative importance of these fundamental components by country and sector. Furthermore, through the Bayesian approach, it is possible to test different hypotheses about the homogeneity of the dynamic behaviour of the aforementioned components with respect to the sector and the country where the firm develops its activity. We find that although both the industry and firm effects are significant, the latter are more important to explain the dynamic evolution of abnormal returns. Specifically, firm effects account for 68% of total variation of the abnormal returns and display a lower degree of persistence with adjustment speeds oscillating at around 34%, while industry effects only account for 9% and have adjustment speeds oscillating between 7% and 8%. However, this pattern is not homogeneous and depends on the sector and country in which the firm carries out its activity. These results highlight the need to take into account both aspects simultaneously in order to analyse the dynamic behaviour of abnormal returns. Copyright © 2014 John Wiley & Sons, Ltd.     

A Generalized Two-Agent Location Problem: Asymmetric Dynamics and Coordination

We generalize a static two-agent location problem into dynamic, asymmetric settings. The dynamics is due to the ability of the agents to move at limited speeds. Since each agent has its own objective (demand) function and these functions are interdependent, decisions made by each agent may affect the performance of the other agent and thus affect the overall performance of the system. We show that, under a broad range of system’s parameters, centralized (system-wide optimal) and non-cooperative (Nash) behavior of the agents are characterized by a similar structure. The timing of these trajectories and the intermediate speeds are however different. Moreover, non-cooperative agents travel more and may never rest and thus the system performance deteriorates under decentralized decision-making. We show that a static linear reward approach, recently developed in Golany and Rothblum (Nav. Res. Logist. 53(1):1–15, 2006), can be generalized to provide coordination of the moving agents and suggest its dynamic modification. When the reward scheme is applied, the agents are induced to choose the system-wide optimal solution, even though they operate in a decentralized decision-making mode.     

Production lot-sizing with dynamic capacity adjustment

In this paper we study a single-item lot-sizing model in which production capacity can be adjusted from time to time. There are a number of different production capacity levels available to be acquired in each period, where each capacity level is assumed to be a multiple of a base capacity unit. To reduce the waste of excess of capacity but guarantee meeting the demand, it is important to decide which level of capacity should be acquired and how many units of the item should be produced for every period in the planning horizon. Capacity adjustment cost incurs when capacity acquired in the current period differs from the one acquired in the previous period. Capacity acquisition costs, capacity adjustment costs, and production costs in each period are all time-varying and depend on the capacity level acquired in that period. Backlogging is allowed. Both production costs and inventory costs are assumed to be general concave. We provide optimal properties and develop an efficient exact algorithm for the general model. For the special cases with zero capacity adjustment costs or fixed-plus-linear production costs, we present a faster exact algorithm. Computational experiments show that our algorithm is able to solve medium-size instances for the general model in a few seconds, and that cost can be reduced significantly through flexible capacity adjustment.     

The Effect of Clone Template Parameters on the Spreading Speeds in CNNs

The aim of this paper is to investigate the effect of clone template parameters on the spreading speeds in cellular neural networks(CNNs). According to the property analysis of spreading speeds of monotone semiflows developed by Yu and Zhang [{\it European Journal of Applied Mathematics}, {\bf 31} (2020), 369-384], we investigate the sign of spreading speeds, continuity and limit cases with no propagation phenomena for CNNs with general output functions where each cell interacts with its 2-neighborhood cell.     

Optimal Paths And Costs Of Adjustment In Dynamic DEA Models: With Application To Chilean Department Stores

In this paper we propose a range of dynamic data envelopment analysis (DEA) models which allow information on costs of adjustment to be incorporated into the DEA framework. We first specify a basic dynamic DEA model predicated on a number of simplifying assumptions. We then outline a number of extensions to this model to accommodate asymmetric adjustment costs, non-static output quantities, non-static input prices, and non-static costs of adjustment, technological change, quasi-fixed inputs and investment budget constraints. The new dynamic DEA models provide valuable extra information relative to the standard static DEA models—they identify an optimal path of adjustment for the input quantities, and provide a measure of the potential cost savings that result from recognising the costs of adjusting input quantities towards the optimal point. The new models are illustrated using data relating to a chain of 35 retail department stores in Chile. The empirical results illustrate the wealth of information that can be derived from these models, and clearly show that static models overstate potential cost savings when adjustment costs are non-zero. This paper arises out the senior author's PhD thesis at the University of New England, Australia. The authors gratefully acknowledge Dr. George E. Battese for his comments on earlier drafts of this work.     

Joint use of DEA and constrained canonical correlation analysis for efficiency valuations involving categorical variables

The research on efficiency valuations has used two distinct approaches. One is the nonparametric approach known as data envelopment analysis (DEA), the other is the parametric approach based on regression analysis or its extension such as constrained canonical correlation analysis (CCCA). Interestingly, a recent study has employed a hybrid approach that cross-fertilizes DEA and CCCA to compensate for the drawbacks of the two methods and capture their positive aspects. This approach first applies DEA to select efficient units and then utilizes CCCA to identify a smooth efficient frontier with the selected efficient units only. We extend it to incorporate a categorical variable that reflects an environmental effect on efficiency performance. The need for considering a categorical variable arises in practice for an equitable efficiency valuation, as illustrated by managerial performance evaluation of the branches of a fast-food company, where the location of branches such as commercial or noncommercial area significantly affects their performance. We demonstrate various possible ways to handle such a categorical variable in the framework of a hybrid approach and characterize each of the methods. Based on this study, we suggest one method that simultaneously utilizes an extension of DEA, referred to as DEA with categorical variable, and CCCA employing a dummy variable, as in multiple regressions with dummy variables. Through an application to the branches of a fast-food company, we show the efficacy of the suggested method in terms of penalizing the advantageous location effect and compensating for the disadvantageous location effect. We also provide some discussions on the limitations underlying the hybrid approach in order to guide a proper use of this approach to the other potential applications.     

Asset liquidity and the valuation of derivative securities

We consider the valuation of European-style derivative securities under limited asset liquidity through the dynamic management of a portfolio of assets effected through continuous transaction. The valuation arises from the optimal realization of a performance index relative to the set of all feasible portfolio trajectories. An approximation procedure based upon the method-of-lines finite element method is developed and analyzed; numerical examples are presented in order to demonstrate the viability of the approach.     

Automation and group structures in certain economic adjustment mechanisms

It is shown that the economic adjustment mechanism developed by Hurwicz and his associates has the structure of automata. It is then shown that certain price adjustment mechanisms, having an acceptability condition, impose a group structure upon the automaton. This condition is a bilinear invariance implied by a budget constraint. Then the automaton is defined by a subgroup, depending on agents' tastes, technologies and strategies, and by the representations of the subgroup imposed by the automaton.     

Lie-algebraic approach for pricing moving barrier options with time-dependent parameters

In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.     

Collective adjustment of pension rights in ALM models

Collective adjustment of pension rights is a way to keep defined benefit systems tenable. In asset liability management (ALM) models presented in the literature these decisions are modeled both at the aggregate level of the liabilities as a whole and at a more detailed level. In this paper we compare the approximate aggregate approach to the accurate detailed approach for the average earnings scheme with conditional indexation. We prove that the aggregate approach leads to one-sided errors. Moreover, we show that for semi-realistic data these biases are considerable.     

对部分线性模型用惩罚最小二乘估计时最优光滑化的注记

部分线性模型也就是响应变量关于一个或者多个协变量是线性的, 但对于其他的协变量是非线性的关系\bd 对于部分线性模型中的参数和非参数部分的估计方法, 惩罚最小二乘估计是重要的估计方法之一\bd 对于这种估计方法, 广义交叉验证法提供了一种确定光滑参数的方法\bd 但是, 在部分线性模型中, 用广义交叉验证法确定光滑参数的最优性还没有被证明\bd 本文证明了利用惩罚最小二乘估计对于部分线性模型估计时, 用广义交叉验证法选择光滑参数的最优性\bd 通过模拟验证了本文中所提出的用广义交叉验证法选择光滑参数具有很好的效果, 同时, 本文在模拟部分比较了广义交叉验证和最小二乘交叉验证的优劣.     

Stabilization of a one‐dimensional wave equation with variable coefficient under non‐collocated control and delayed observation

In this paper, we consider stabilization of a 1‐dimensional wave equation with variable coefficient where non‐collocated boundary observation suffers from an arbitrary time delay. Since input and output are non‐collocated with each other, it is more complex to design the observer system. After showing well‐posedness of the open‐loop system, the observer and predictor systems are constructed to give the estimated state feedback controller. Different from the partial differential equation with constant coefficients, the variable coefficient causes mathematical difficulties of the stabilization problem. By the approach of Riesz basis property, it is shown that the closed‐loop system is stable exponentially. Numerical simulations demonstrate the effect of the stable controller. This paper is devoted to the wave equation with variable coefficients generalized of that with constant coefficients for delayed observation and non‐collocated control.     

On the complexity of simultaneous price-quantity adjustment processes

While the Walrasian price tâtonnement represents the traditional dynamic process in the general equilibrium context with and without production, Walras and other classics designed the process exclusively for pure exchange economies. In productive economies, the short-run output adjustment of existing firms and the entry/exit of firms should be modeled as well. So-called cross-dual processes which represent the classical approach to the dynamics of productive economies are discussed and extended. Complex motion can emerge in a discrete-time version of the original two-dimensional system when the aggregate demand function has a non-standard shape. A simultaneous process of price and short-run quantity adjustment with free entry and exit of competitive firms in a single market with a continuum of firms can generate closed orbits via a Hopf bifurcation when the slope of the demand function is positive at equilibrium. When the continuum economy is replaced by an economy with a finite number of firms, noisy limit cycles and complicated behavior can be observed.