On Minimally-supported <Emphasis Type="Italic">D</Emphasis>-optimal Designs for Polynomial Regression with Log-concave Weight Function

This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions. Many commonly used weight functions in the design literature are log-concave. For example, and exp(−x ²) in Theorem 2.3.2 of Fedorov (Theory of optimal experiments, 1972) are all log-concave. We show that the determinant of information matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be constructed efficiently by cyclic exchange algorithm.     

$$\mathcal{D}$$-optimal Minimum Support Mixture Designs in Blocks

An easy method to construct efficient blocked mixture experiments in the presence of fixed and/or random blocks is presented. The method can be used when qualitative variables are involved in a mixture experiment as well. The resulting designs are -optimal in the class of minimum support designs. It is illustrated that the minimum support designs are more efficient than orthogonally blocked mixture experiments presented in the literature and only slightly less efficient than -optimal designs.     

Variation diminishing property of densities of uniform generalized order statistics

Let f _*,r , r ≥ 1, denote the density function of rth uniform generalized order statistics as defined by Kamps (1995) or Cramer and Kamps (2003). We prove the following variation diminishing property: the number of zeros in (0,1) of any linear combination does not exceed the number of sign changes in the sequence (a ₁, . . . ,a _r ). This result is applied to study monotonicity and convexity properties of f _*,r .     

Parsing Work Environments Along the Dimensions of Sexual and Non-Sexual Harassment: Drawing Lines in Office Sand

Laws addressing harassment at work have evolved considerably since court systems first recognized that (sexual) harassment is illegal. Now, managers must worry about protected classes other than sex (e.g., race, age, etc.), and the effects of harassment on bystanders as well as victims (i.e., ambient harassment). Understanding these newer conceptualizations of workplace harassment is critical for mangers dealing with an increasingly complex array of possible work environments, only some of which are illegal. Toward this end, we present a taxonomy of eight possible work environments, created by parsing the legal definition of sexual harassment (i.e., the first-recognized type of hostile work environment). The taxonomy illustrates the evolution of law in this area, and highlights the multidimensional nature of workplace harassment. Also discussed are potential complications arising from how a reasonable person and a victim might interpret behavior. Managers using the taxonomy may better assess whether their work environments have crossed the line, or facilitate movement from less- to more-desirable work environments.

The optimal asset allocation of the main types of pension funds: a unified framework

The existing literature deals with the optimal investment strategy of defined benefit (DB) or defined contribution (DC) pension plans. This article’s objective is to compare the optimal policies of different types of pension plans. This is done by first defining an original framework, which is based on the distinction between the nature of the guarantee—which can be internal or external—offered by or to a pension fund. This framework allows to establish links between optimization programs of DC, DB and targeted money purchase schemes. The case of an internal guarantee appears as a standard portfolio insurer’s problem. The second kind of guarantee, not analyzed in the literature yet with regard to the resulting optimal policy, is characterized by the existence of an option in the final wealth definition. Four funds are present in the internal guarantee optimal allocation: the speculative component, the preference independent guarantee- and contribution-hedge terms and the preference dependent state variable-hedge fund. The external guarantee program, solved with an original method using the principles of standard options theory, yields an optimal policy incorporating the delta of the option embodied in the final wealth definition. The conclusion is that the resulting optimal portfolio policy becomes riskier.

The tactical and strategic value of hedge fund strategies: a cointegration approach

This paper analyzes long-term comovements between hedge fund strategies and traditional asset classes using multivariate cointegration methodology. Since cointegrated assets are tied together over the long run, a portfolio consisting of these assets will have lower long-term volatility. Thus, if the presence of cointegration lowers uncertainty, risk-averse investors should prefer assets that are cointegrated. Long-term (passive) investors can benefit from the knowledge of cointegrating relationships, while the built-in error correction mechanism allows active asset managers to anticipate short-run price movements. The empirical results indicate there is a long-run relationship between specific hedge fund strategies and traditional financial assets. Thus, the benefits of different hedge fund strategies are much less than suggested by correlation analysis and portfolio optimization. However, certain strategies combined with specific stock market segments offer portfolio managers adequate diversification potential, especially in the framework of tactical asset allocation.

Technological knowledge as an essential facility

The economics of regulation has articulated the notions of essential facility and mandated interconnection. Their application to the governance of technological knowledge can be fruitful especially when implemented by the adoption of a compensatory liability rule and the parallel reduction in the exclusivity of patents. Because knowledge is at the same time an output and an input in the production of new knowledge, exclusivity, traditionally associated to patents, is the cause of actual knowledge rationing with major drawbacks in terms of both static and dynamic efficiency. This institutional innovation can improve the governance of technological knowledge and increase both its rates of dissemination and generation.

Property rights and information flows: a simulation approach

With the growth of the information economy, the proportion of knowledge-intensive goods to total goods is constantly increasing. Lessig (The future of ideas: the fate of the commons in a connected world. Vintage, New York 2001) has argued that IPRs have now become too favourable to existing producers and that their ‘winner-take-all’ characteristics are constraining the creators of tomorrow. In this paper we look at how variations in IPRs regimes might affect the creation and social cost of new knowledge in economic systems. Drawing on a conceptual framework, the Information Space or I-Space to explore how the uncontrollable diffusibility of knowledge relates to its degree of structure, we deploy an agent-based modelling approach to explore the issue of IPRs. We take the ability to control the diffusibility of knowledge as a proxy measure for an ability to establish property rights in such knowledge. Second, we take the rate of obsolescence of knowledge as a proxy measure for the degree of turbulence induced by different regimes of technical change. Then we simulate the quantity and cost to society of new knowledge under different property right regimes.

Existence of Sparsely Supported Correlated Equilibria

We show that every N-player K ₁ × ... × K _N game possesses a correlated equilibrium with at least zero entries. In particular, the largest N-player K × ... × K games with unique fully supported correlated equilibrium are two-player games. We thank an anonymous referee for most useful comments. The first author acknowledges financial support from Spanish Ministry of Science and Technology, grant SEJ2004-03619, and in form of a Ramón y Cajal fellowship. The second author acknowledges support by the PASCAL Network of Excellence under EC grant no.506778, as well as from Spanish Ministry of Science and Technology and FEDER, grant BMF2003-03324. Both authors also acknowledge financial support from BBVA grant “Aprender a jugar.”     

Passive learning: a critique by example

In models of learning by experimentation that exhibit signal dependence, a benchmark using a passive learner has been proposed. The use of this benchmark is flawed – first, passive learning does not disentangle the effects of knowing that beliefs, as well as other state variables, might change, and we address this issue directly by introducing a naïve learner. Secondly, and more tellingly, passive learning does not do what it is supposed to do, namely help measure the gains from active experimentation; the naïve learner enables us to illustrate this point in the context of a particular example.