Equilibrium in abstract economies without ordered preferences

We extend a theorem of G. Debreu on the existence of equilibrium in a generalized N-person game (‘A Social Equilibrium Existence Theorem’). Applying standard techniques the result can be used to prove the existence of equilibrium in economies with interdependent preferences, price-dependent preferences and preferences which may be both non-transitive and non-complete. This generalizes a recent theorem of A. Mas-Colell.     

Clustering consistency analysis

Cluster analysis is a frequently used technique in marketing as a method to develop partitions or classifications for market segmentation, product positioning, test market selection, etc. Because of the vast diversity in the assortment of clustering algorithms available, it is often times not obvious which algorithm or technique should be employed. It is often recommended that the marketer perform more than one cluster analysis on the same data set and compare representations as a reliability check. A methodology for evaluating the consistency of different clusterings is introduced via contingency table analysis by log-linear models. In addition, insight is provided as to selecting a “best” representative clustering by examining Stewart and Love's (1968) redundancy measures. Bell Laboratories     

Note on the behavior of residual security returns for winner and loser portfolios

Portfolios are formed directly and exclusively upon residual return behavior in the months prior to portfolio formation. The empirical behavior of residual return in the post-formation period is then examined. Based upon the overall time period studied (1932 through 1977), the average residual return is essentially zero in the months subsequent to the portfolio formation. However, systematic (i.e., non-zero) residual behavior is observed in particular years. Moreover, the results suggest the possibility that ‘abnormal’ returns observed after certain events (e.g., earnings announcements) may at least in part reflect more general phenomena associated with being ‘winners’ and ‘losers’ in terms of residual returns in the months previous to the event.     

THE INFLUENCE OF OFFERING YIELD ON UNDERWRITING SPREAD

This paper presents a model that explains variation in underwriting spreads among primary issues of investment quality bonds and assesses the impact that offering yields have on underwriting spreads. The results indicate that issues having higher (lower) offering yields pay lower (higher) underwriting spreads.     

GRAFTED POLYNOMIALS AS APPROXIMATING FUNCTIONS

The use of segments of polynomials to approximate production surfaces and time-series trends is described and illustrated. These segmented curves are restricted to be continuous and have a continuous derivative(s) at the join points.