Self-organization and social science

Abstract Complexity science and its methodological applications have increased in popularity in social science during the last two decades. One key concept within complexity science is that of self-organization. Self-organization is used to refer to the emergence of stable patterns through autonomous and self-reinforcing dynamics at the micro-level. In spite of its potential relevance for the study of social dynamics, the articulation and use of the concept of self-organization has been kept within the boundaries of complexity science and links to and from mainstream social science are scarce. These links can be difficult to establish, even for researchers working in social complexity with a background in social science, because of the theoretical and conceptual diversity and fragmentation in traditional social science. This article is meant to serve as a first step in the process of overcoming this lack of cross-fertilization between complexity and mainstream social science. A systematic review of the concept of self-organization and a critical discussion of similar notions in mainstream social science is presented, in an effort to help practitioners within subareas of complexity science to identify literature from traditional social science that could potentially inform their research.

Multivariate Appoximations to Portfolio Return Distribution

This article proposes a three-step procedure to estimate portfolio return distributions under the multivariate Gram-Charlier (MGC) distribution. The method combines quasi maximum likelihood (QML) estimation for conditional means and variances and the method of moments (MM) estimation for the rest of the density parameters, including the correlation coefficients. The procedure involves consistent estimates even under density misspecification and solves the so-called ‘curse of dimensionality’ of multivariate modelling. Furthermore, the use of a MGC distribution represents a flexible and general approximation to the true distribution of portfolio returns and accounts for all its empirical regularities. An application of such procedure is performed for a portfolio composed of three European indices as an illustration. The MM estimation of the MGC (MGC-MM) is compared with the traditional maximum likelihood of both the MGC and multivariate Student’s t (benchmark) densities. A simulation on Value-at-Risk (VaR) performance for an equally weighted portfolio at 1% and 5% confidence indicates that the MGC-MM method provides reasonable approximations to the true empirical VaR. Therefore, the procedure seems to be a useful tool for risk managers and practitioners.