Measures of risk aversion with expected and nonexpected utility

In the expected utility case, the risk-aversion measure is given by the Arrow-Pratt index. Three proposals of a risk-aversion measure for the nonexpected utility case are examined. The first one sets “the second derivative of the acceptance frontier as a measure of local risk aversion.” The second one takes into account the concavity in the consequences of the partial derivatives of the preference function with respect to probabilities. The third one measures risk aversion through the ratio between the risk premium and the standard deviation of the lottery. The third proposal catches the main feature of risk aversion, while the other two proposals are not always in accordance with the same crude definition of risk aversion, by which there is risk aversion when an agent prefers to get the expected value of a lottery rather than to participate in it.     

The risk aversion measure without the independence axiom

The risk premium (conveniently normalized) is defined as the measure of risk aversion. This measure does not require any relevant assumption in the theory of choice under uncertainty except the existence of a certainty equivalent. In particular, the independence axiom is not required. The measure of risk aversion of an action is provided not only for the case with one commodity and two consequences but also for the case with many commodities and consequences. The measure of mean risk aversion of all actions with given consequences is introduced and the local measure of risk aversion is obtained by making all these consequences approach the consequence under consideration. This measure is demonstrated to be zero when the von Neumann-Morgenstern utility function exists. In this case a measure of risk aversion of the second order is introduced, which turns out to be equal to the Arrow-Pratt absolute index when there is only one commodity and similar to the generalized measures proposed by several authors when there are many commodities and two consequences.Helpful comments by I. Gilboa and suggestions by the referee are gratefully acknowledged.     

Board characteristics effects on performance in family and non-family business: a multi-theoretical approach

This paper examines the role of the board of directors in influencing the value of Italian listed firms from 2003 to 2013. In particular, employing agency, stewardship and resource dependence theories, the study aims to compare board characteristics in family and non-family firms and define the theory that best applies to family firms. Empirical results show that the presence of CEO duality and busy directors has a positive effect on the value of family firms, while gender diversity has a negative impact on the value when a member of the family leads a family firm. Conversely, the size of the board positively affects the value of non-family firms. Our main findings suggest the prevalence, in family firms, of the benefits of the board structure argued by stewardship and resource dependence theories rather than the disadvantages expected from agency theory.     

The role of passing network indicators in modeling football outcomes: an application using Bayesian hierarchical models

AStA Advances in Statistical Analysis - Passes are undoubtedly the more frequent events in football and other team sports. Passing networks and their structural features can be useful to evaluate...