New classes of improved confidence intervals for the variance of a normal distribution

Two new classes of improved confidence intervals for the variance of a normal distribution with unknown mean are constructed. The first one is a class of smooth intervals. Within this class, a subclass of generalized Bayes intervals is found which contains, in particular, the Brewster and Zidek-type interval as a member. The intervals of the second class, though non-smooth, have a very simple and explicit functional form. The Stein-type interval is a member of this class and is shown to be empirical Bayes. The construction extends Maruyama’s (Metrika 48:209–214, 1998) point estimation technique to the interval estimation problem.     

Diversity and relative arbitrage in equity markets

An equity market is called diverse if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itô-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of weak diversity and asymptotic weak diversity) in precise terms. We show that diversity is possible to achieve, but delicate. Several examples are provided which illustrate these notions and show that weakly-diverse markets contain relative arbitrage opportunities: it is possible to outperform or underperform such markets over any given time-horizon. The existence of this type of relative arbitrage does not interfere with the development of contingent claim valuation, and has consequences for the pricing of long-term warrants and for put-call parity. Several open questions are suggested for further study.Received: January 2004, Mathematics Subject Classification (2000): 60H10, 91B28; 60J55JEL Classification: G10We are grateful for the helpful remarks offered by seminar audiences at Columbia, Yale, Princeton, the Sloan School of MIT, Boston University, the Mathematical Institute in Oberwolfach, and the Universities of Athens, Connecticut/Storrs and Texas/Austin. Special thanks go to Professors Jérôme Detemple, Julien Hugonnier, Ralf Korn, Andrew Lo, Mark Lowenstein and Steven Shreve. We are also indebted to Dr. Adrian Banner for a number of discussions that helped sharpen our thinking about these problems, and to the referees and editors for suggestions that improved the exposition. A significant part of this work was completed in the spring semester of 2002, while the second author was on sabbatical leave at the Cowles Foundation for Research in Economics, Yale University. He is grateful to the Foundation for its hospitality.     

Business Unethicality as an Impediment to Consumer Trust: The Moderating Role of Demographic and Cultural Characteristics

The article reports the findings of a study conducted among 387 consumers regarding their perceptions of the unethicality of business practices of firms and how these affect their response behavior, in terms of trust, satisfaction, and loyalty. The study confirmed that high levels of perceived corporate unethicality decrease consumer trust. This in turn reduces consumer satisfaction, which ultimately has negative effects on customer loyalty. It was also revealed that, although both consumer gender and urbanity have a moderating effect on the link between perceived unethicality and trust, the age group and level of education of the consumer did not exhibit such an effect. With regard to consumer cultural characteristics, both high uncertainty avoidance and low individualism were found to increase the negative impact of business unethicality on trust, as opposed to power distance and masculinity that did not have any moderating effect on this relationship. Implications for managers are extracted from the study findings, as well as directions for future research.