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The variance targeting estimator (VTE) for generalized autoregressive conditionally heteroskedastic (GARCH) processes has been proposed as a computationally simpler and misspecification-robust alternative to the quasi-maximum likelihood estimator (QMLE). In this paper we investigate the asymptotic behavior of the VTE when the stationary distribution of the GARCH process has infinite fourth moment. Existing studies of historical asset returns indicate that this may be a case of empirical relevance. Under suitable technical conditions, we establish a stable limit theory for the VTE, with the rate of convergence determined by the tails of the stationary distribution. This rate is slower than that achieved by the QMLE. The limit distribution of the VTE is nondegenerate but singular. We investigate the use of subsampling techniques for inference, but find that finite sample performance is poor in empirically relevant scenarios.

The potential advantage of extreme value theory in modeling management phenomena is the central theme of this paper. The statistics of extremes have played only a very limited role in management studies despite the disproportionate emphasis on unusual events in the world of managers. An overview of this theory and related statistical models is presented, and illustrative empirical examples provided.

Rapid stock market growth without real economic back-up has led to the 2015 Chinese Stock Market Crash with thousands of stocks hitting the down limit simultaneously multiple times. The authors provide a detailed analysis of structural breaks in heavy-tailedness and asymmetry properties of returns in Chinese A-share markets due to the crash using recently proposed robust approaches to tail index inference. The empirical analysis points out to heavy-tailedness properties often implying possibly infinite second moments and also focuses on gain/loss asymmetry in the tails of daily returns on individual stocks. The authors further present an analysis of the main determinants of heavy-tailedness in Chinese financial markets. It points out to liquidity and company size as being the most important factors affecting the returns’ heavy-tailedness properties. At the same time, the authors do not observe statistically significant differences in tail indices of the returns on A-shares and the coefficients on factors affecting them in the pre-crisis and post-crisis periods.

Standard financial risk management practices proved unable to provide an adequate understanding and a timely warning of the financial crisis. In particular, the theoretical foundations of risk management and the statistical calibration of risk models are called into question. Policy makers and practitioners respond by looking for new analytical approaches and tools to identify and address new sources of financial risk. Financial markets satisfy reasonable criteria of being considered complex adaptive systems, characterized by complex financial instruments and complex interactions among market actors. Policy makers and practitioners need to take both a micro and macro view of financial risk, identify proper transparency requirements on complex instruments, develop dynamic models of information generation that best approximate observed financial outcomes, and identify and address the causes and consequences of systemic risk. Complexity analysis can make a useful contribution. However, the methodological suitability of complexity theory for financial systems and by extension for risk management is still debatable. Alternative models drawn from the natural sciences and evolutionary theory are proposed.

This chapter discusses the emerging network science approach to the study of complex adaptive systems and applies tools derived from statistical physics to the analysis of tourism destinations. The authors provide a brief history of network science and the characteristics of a network as well as different models such as small world and scale free networks, and dynamic properties such as resilience and information diffusion. The Italian resort island of Elba is used as a case study allowing comparison of the communication network of tourist organizations and the virtual network formed by the websites of these organizations. The study compares the parameters of these networks to networks from the literature and to randomly created networks. The analyses include computer simulations to assess the dynamic properties of these networks. The results indicate that the Elba tourism network has a low degree of collaboration between members. These findings provide a quantitative measure of network performance. In general, the application of network science to the study of social systems offers opportunities for better management of tourism destinations and complex social systems.

Unfortunately, the answers given are thoroughly embedded in the physics-inspired view of the financial economy as a stable and an equilibrium seeking system. In such a view, if some changes do occur in the financial markets, those changes present no discontinuities and the model has ample time to react by slowly adjusting risk forecasts as the volatility rises. As almost everybody in the world by now knows, currently accepted risk models have time and again shown their inability to deal with financial market reality. Frequent talk of ‘hundred year floods’ and ‘rise in correlations’ not only suggests frequent failures of a theory, but also the inability of the theory to learn from past mistakes by incorporating new data. The crash of 2008, completely unforeseen by all traditional risk systems, should serve as the final wake-up call to re-examine the foundations of the old paradigm and consider how sound they really are.

The goals of this chapter are three-fold: (1) to outline some broad empirical regularities concerning how drug problems evolve over time, (2) to sketch some plausible mechanisms for ways in which aspects of that variation might be endogenous, and (3) to review two classes of dynamic models of drug use that have implications for how policy should vary over a drug epidemic.