Model selection bias and Freedman’s paradox

In situations where limited knowledge of a system exists and the ratio of data points to variables is small, variable selection methods can often be misleading. Freedman (Am Stat 37:152–155, 1983) demonstrated how common it is to select completely unrelated variables as highly “significant” when the number of data points is similar in magnitude to the number of variables. A new type of model averaging estimator based on model selection with Akaike’s AIC is used with linear regression to investigate the problems of likely inclusion of spurious effects and model selection bias, the bias introduced while using the data to select a single seemingly “best” model from a (often large) set of models employing many predictor variables. The new model averaging estimator helps reduce these problems and provides confidence interval coverage at the nominal level while traditional stepwise selection has poor inferential properties.     

Mean–semivariance portfolio selection under probability distortion

We formulate and study a mean–semivariance portfolio selection problem in continuous time when the probability is distorted by a nonlinear transformation. We give necessary and sufficient conditions for the feasibility and the existence of optimal strategies, respectively, and present the general form of optimal solutions when they exist. In sharp contrast with the previously established result that the infimum of the problem is not attainable when there is no probability distortion, we show that the infimum can be achieved with proper probability distortions. Finally, for a number of interesting cases we derive the optimal solutions in closed forms whenever they exist.     

Some consequences of Rado’s selection lemma

We prove in set theory without the Axiom of Choice, that Rado’s selection lemma ( ${\mathbf{RL}}$ ) implies the Hahn-Banach axiom. We also prove that ${\mathbf{RL}}$ is equivalent to several consequences of the Tychonov theorem for compact Hausdorff spaces: in particular, ${\mathbf{RL}}$ implies that every filter on a well orderable set is included in a ultrafilter. In set theory with atoms, the “Multiple Choice” axiom implies ${\mathbf{RL}}$ .     

Pattern selection in the 2D FitzHugh–Nagumo model

We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.

     

The curve selection lemma and the Morse–Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C ^r function , we have

Mean–Variance portfolio selection in presence of infrequently traded stocks

This paper deals with a mean–variance optimal portfolio selection problem in presence of risky assets characterized by low-frequency trading and, therefore, low liquidity. To model the dynamics of illiquid assets, we introduce pure-jump processes. This leads to the development of a portfolio selection model in a mixed discrete/continuous time setting. We pursue the twofold scope of analyzing and comparing either long-term investment strategies as well as short-term trading rules. The theoretical model is analyzed by applying extensive Monte Carlo experiments, in order to provide useful insights from a financial perspective.     

Natural selection: A concept in need of some evolution?

In some respects natural selection is a quite simple theory, arrived at through the logical integration of three propositions (the presence of variation within natural populations, an absolutely limited resources base, and procreation capacities exceeding mere replacement numbers) whose individual truths can hardly be denied. Its relation to the larger subject of evolution, however, remains problematic. It is suggested here thata scaling‐down of the meaning of natural selection to “the elimination of the unfit,” as originally intended by Alfred Russel Wallace (1823–1913), might ultimately prove a more effective means of relating it to larger‐scale, longer‐term, evolutionary processes. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

A selection algorithm for ∊-optimal policies in undiscounted maekovian decision problems

In many real-world problems it is interesting to know the whole set of optimal or e-optimal policies of a finite-state, finite-action undiscounted Markovian Decision Problem. For finding all optimal or e-optimal policies of such a given problem we present in many real-world problems it is interesting to know the whole set of optimal or e-optimal policies of a finite-state, finite-action undiscounted Markovian Decision Problem. For finding all optimal or e-optimal policies of such a given problem we present sideration of subproblems which will be solved by Howard'S policy iteration.     

Customization competition between branded firms: Continuous extension of product line from core product

We study a competition of product customization between two branded firms by a game-theoretic approach. Firms produce products with two attributes: one attribute indicates a characteristic with regard to “function” or “design” of a product and the other indicates “taste” or “flavor” of the product, which reflects consumers’ brand/taste preferences. Two branded firms have their own specific core products and our customization is defined as a continuous extension of their product line from the core product only along the “function” attribute. In particular, we allow asymmetric positions of core products, which may create the position advantage/disadvantage between firms. We suppose that consumers incur their selection costs with regard to finding their most favorable item among a rich variety of products and firms incur their customizing costs with regard to extending their product lines. We first show that in the equilibrium, branded firms should fundamentally adopt their customizations to cover the center space in the market as far as possible, regardless of the position of the competitor’s core product. Therefore, the position of the core product contributes to the creation of a competitive advantage: when one firm’s core product is located more closely to the center of the market than the competitor’s, its customization can always cover more range of the center space in the market, while keeping its degree of customization smaller than the competitor’s. Furthermore, we show some implications of unit-cost improvement: in a short run, a firm is better off concentrating on the improvement of the unit selection cost rather than the unit customizing cost. In contrast, in a long run, both firms can benefit from the improvement of the unit customizing cost.     

To reveal or not to reveal? Strategic disclosure of private information in negotiation

Within the bargaining literature, it is widely held that negotiators should never reveal information that will lead to disclosure of their reservation prices. We analyze a simple bargaining and search model in which the informed buyer can choose to reveal his cost of searching for an outside price (which determines his reservation price) to the uninformed seller. We demonstrate that buyers can be made better off by revealing their search cost. More interestingly, we also find that, depending on the assumed distribution of search costs, sometimes buyers with relatively low search costs should reveal their private information whereas in other cases buyers with relatively high search costs should do so. We then test our model experimentally and find that subjects’ behavior is not entirely consistent with theoretical predictions. In general, bargainers’ behavior is better explained by a bounded rationality model similar to “fictitious play”.     

Risky asset allocation and consumption rule in the presence of background risk and insurance markets

This study examines joint decisions regarding risky asset allocation and consumption rate for a representative agent in the presence of background risk and insurance markets. Contrary to the conclusion of the “mutual fund separation theorem”, we show that the optimal risky asset mix will reflect an agent’s risk attitude as long as background risk is not independent of investment risk. This result can, however, be used to solve the “riskyasset allocation puzzle”. We also unveil that optimal insurance to shift background risk is determined through establishing a hedging portfolio against investment risk and is an arrangement maintaining the balance between growth and volatility of expected consumption. Because the optimal insurance we obtain generally leads to a smoother consumption path, it may plausibly explain the “equity premium puzzle” in the financial literature.     

Evaluating and selecting the supplier in detergent production industry using hierarchical fuzzy TOPSIS

Supply chain management has increasingly attracted attention as a systematic approach to integrate the supply chain in order to planning and controlling the materials and information from suppliers to customers. One of the most important issues in supply chain management is selection of the appropriate supplier which has significant effect on purchasing cost decrease and increase in the organization’s competition ability. Selection of the best supplier is naturally complex with no definite structure, and dependent on the type of suppliers’ activity. In the process of decision making about suppliers and many qualitative and quantitative performance indicators such as quality, price, flexibility, and due date should be considered. Then, the supplier selection problem is a multi-criteria decision making problem where numerous methods have been proposed to solve this problem so far. In the current paper, four suppliers of imported raw material “Tripolyphosphate (TPP)” (primary material to produce the detergent powder with a case study in Iran) are evaluated based on 25 effective criteria using the hierarchical fuzzy TOPSIS (HFTOPSIS) approach.     

Optimizing referral reward programs under impression management considerations

We examine referral reward programs (RRP) that are intended for a service firm to encourage its current customers (inductors) to entice their friends (inductees) to purchase the firm’s service. By considering the interplay among the firm, the inductor, and the inductee, we solve a “nested” Stackelberg game so as to determine the optimal RRP in equilibrium. We determine the conditions under which it is optimal for the firm to reward the inductor only, reward the inductee only, or reward both. Also, our results suggest that RRP dominates direct marketing when the firm’s current market penetration or the inductor’s referral effectiveness is sufficiently high. We then extend our model to incorporate certain key impression management factors: the inductor’s intrinsic reward of making a positive impression by being seen as helping a friend, the inductor’s concerns about creating a negative impression when making an incentivized referral, and the inductee’s impression of the inductor’s credibility when an incentive is involved. In the presence of these impression management factors, we show that the firm should reward the inductee more and the inductor less. Under certain conditions, it is optimal for the firm to reward neither the inductor nor the inductee so that the optimal RRP relies purely on unincentivized word of mouth.     

Robust portfolio selection involving options under a “ marginal+joint ” ellipsoidal uncertainty set

In typical robust portfolio selection problems, one mainly finds portfolios with the worst-case return under a given uncertainty set, in which asset returns can be realized. A too large uncertainty set will lead to a too conservative robust portfolio. However, if the given uncertainty set is not large enough, the realized returns of resulting portfolios will be outside of the uncertainty set when an extreme event such as market crash or a large shock of asset returns occurs. The goal of this paper is to propose robust portfolio selection models under so-called “ marginal+joint” ellipsoidal uncertainty set and to test the performance of the proposed models. A robust portfolio selection model under a “marginal + joint” ellipsoidal uncertainty set is proposed at first. The model has the advantages of models under the separable uncertainty set and the joint ellipsoidal uncertainty set, and relaxes the requirements on the uncertainty set. Then, one more robust portfolio selection model with option protection is presented by combining options into the proposed robust portfolio selection model. Convex programming approximations with second-order cone and linear matrix inequalities constraints to both models are derived. The proposed robust portfolio selection model with options can hedge risks and generates robust portfolios with well wealth growth rate when an extreme event occurs. Tests on real data of the Chinese stock market and simulated options confirm the property of both the models. Test results show that (1) under the “ marginal+joint” uncertainty set, the wealth growth rate and diversification of robust portfolios generated from the first proposed robust portfolio model (without options) are better and greater than those generated from Goldfarb and Iyengar’s model, and (2) the robust portfolio selection model with options outperforms the robust portfolio selection model without options when some extreme event occurs.     

Exploring the critical pillars and causal relations within the NRI: An innovative approach

The Global Information Technology Report released by the World Economic Forum (WEF) has employed networked readiness index (NRI) to measure the global competitiveness of a country’s information and communication technologies (ICT) diffusion. The final NRI overall scores were measured by an arithmetic mean aggregation of the composite pillars scores, which implicitly assumed that all the pillars have constant weights. The Report did not explore the critical pillars and causal relations for better decision making. To add values to this Report, the objective of this paper is to propose an innovative approach by using data mining techniques and partial least squares path modeling to scrutinize the critical pillars within the NRI and to further explore the causal relations amongst them. An empirical analysis based on the latest Report (2009-2010) is carried out. The results show that “business usage,” “business readiness,” and “market environment” are the three root drivers—critical pillars to manipulate the NRI overall scores; whereas “government readiness,” which is further mostly affected by the “government usage,” is the foremost enabler to the NRI overall scores. Based on the results, policy makers are suggested to allocate limited resources with priority to the three root drivers and one foremost enabler to frog-leap the global competitiveness of national ICT diffusion.     

Asymptotic analysis for a downside risk minimization problem under partial information

We give an analytic characterization of a large-time “downside risk” probability associated with an investor’s wealth. We assume that risky securities in our market model are affected by “hidden” economic factors, which evolve as a finite-state Markov chain. We formalize and prove a duality relation between downside risk minimization and the related risk-sensitive optimization. The proof is based on an analysis of an ergodic-type Hamilton–Jacobi–Bellman equation with large (exponentially growing) drift.     

To ask or not to ask,that is the question

Applicants for credit have to provide information for the risk assessment process. In the current conditions of a saturated consumer lending market, and hence falling “take” rates, can such information be used to assess the probability of a customer accepting the offer?     

Strategic multi-store opening under financial constraint

This paper analyzes strategic store openings in a situation in which firms can open multiple stores depending on the financial constraints of the firm. Specifically, given any upper limit of the number of store openings that two potentially symmetric firms can open, they sequentially determine the number of store openings, including their locations, to maximize their profits. As a result of our analysis in a microeconomic framework, we show that the equilibrium strategy can be wholly classified into only two following opposite strategies according to the level of their financial constraints involved. When firms can afford to invest significant amounts of money in the market, the leader chooses “segmentation strategy,” in which a part of the market can be monopolized by opening a chain of multiple stores and deterring the follower’s entry. In contrast, when the leader has a severe financial constraint so that it can only monopolize less than half of the market, the leader chooses “minimum differentiation strategy,” where firms open each of their stores at exactly the same point as the rival’s. Under this strategy, the leader necessarily captures just half of the market. Furthermore, we show that regardless of potential symmetry between firms, both first and second mover advantages in terms of profit can occur in the equilibrium.