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© 2017 Elsevier B.V.The article presents the robust estimates of extreme movements and heavy-tailedness properties for Russian stock indices returns before and after sanctions were introduced. The obtained results show that almost for all sectoral indices there was a statistically significant increase in volatility. At the same time there is not enough evidence of structural breaks in heavy-tailedness, though some indications of heavier both right and left tails in the post-imposition period can be observed for some indices. However, we cannot with complete certainty directly link the increase in heavy-tailedness with the imposed sanctions. The latter to a considerable extent could be caused by higher country-specific risks due to geopolitical tensions as well as oil prices volatility. Whatever is the cause, any increases in heavy-tailedness can have grave consequences for corporate management, economic modeling and financial stability analysis.

We show that diversification does not reduce Value-at-Risk for a large class of dependent heavy tailed risks. The class is characterized by power law marginals with tail exponent no greater than one and by a general dependence structure which includes some of the most commonly used copulas.

Focusing on the model of demand-driven innovation and spatial competition over time in Jovanovic and Rob (1987), we study the effects of the robustness of estimators employed by firms to make inferences about their markets on the firms’ growth patterns. We show that if consumers’ signals in the model are moderately heavy-tailed and the firms use the sample mean of the signals to estimate the ideal product, then the firms’ output levels exhibit positive persistence. In such a setting, large firms have an advantage over their smaller counterparts. These properties are reversed for signals with extremely heavy-tailed distributions. In such a case, the model implies anti-persistence in output levels, together with a surprising pattern of oscillations in firm sizes, with smaller firms being likely to become larger ones next period, and vice versa. We further show that the implications of the model under moderate heavy-tailedness continue to hold under the only assumption of symmetry of consumers’ signals if the firms use a more robust estimator of the ideal product, the sample median.

The wetlands of the Amudarya River delta in Uzbekistan provide valuable ecosystem services to the local human population which has suffered severely from the loss of the Aral Sea, desertification and the post-soviet socio-economic transition. The region is also particularly vulnerable to the impacts of climate change as a recent severe drought has shown. In this contribution, we assess the potential and implications of incorporating environmental flows into management of the Amudarya River for improving the provision of wetland ecosystem services and enhancing resilience of the social-ecological system to river runoff uncertainty. Our assessment is based on analyses of 1) the current vulnerability of deltaic wetlands to years of low water availability, 2) expected regional climate change and its impact on water flows to the wetlands, and 3) alternative water use options to enhance environmental flows under a changing climate. The results provide a ranking of these options with respect to their benefits for the provision of environmental flows and implications for agriculture. Their realization, however, poses challenges that cannot be tackled by technical interventions of redistribution and efficiency increase alone but call for institutional changes and moves towards multi-purpose water use. The diversification of impacts and livelihood options would allow enhancing the resilience of the social-ecological system to climate or socio-politically induced changes in water flow.

We obtain estimates for the best constant in the Rosenthal inequality E | ∑ i = 1 n ξ i | 2 m ⩽ C ( 2 m ) max ( ∑ i = 1 n E ξ i 2 m , ( ∑ i = 1 n E ξ i 2 ) m ) for independent random variables ξ 1 , … , ξ n with l zero first odd moments, l ⩾ 1 . The estimates are sharp in the extremal cases l = 1 and l = m , that is, in the cases of random variables with zero mean and random variables with m zero first odd moments.

In this paper, we present a method that allows one to obtain a number of sharp inequalities for expectations of functions of infinite-degree U -statistics. Using the approach, we prove, in particular, the following result: Let D be the class of functions f : R+ → R+ such that the function f( x+ z) − f( x)is concave in x ∈ R+ for all z ∈ R+. Then the following estimate holds: Ef m

We obtain an explicit representation for joint distribution of two-valued random variables with given marginals and for a copula corresponding to such random variables. The results are applied to prove a characterization of r-independent two-valued random variables in terms of their mixed first moments. The characterization is used to obtain an exact estimate for the number of almost independent random variables that can be defined on a discrete probability space and necessary conditions for a sequence of r-independent random variables to be stationary.

In the present paper, we obtain the explicit expression for the best constant in the Rosenthal inequality for nonnegative random variables.

We identify new structural channels for the transmission of shocks in emerging currencies, and develop a model in which shock propagations evolving from domestic emerging stock markets, liquidity (banks’ credit default swaps), credit risk (Volatility Index) and growth (commodity prices) channels disseminate to emerging market foreign exchanges. We quantify joint downside risks and document that these asset classes tend to experience concurrent extreme shocks. We measure the time-varying shock spillover intensities to ascertain a significant increase in cross-asset linkages during periods of high volatility which is over and above any expected economic fundamentals, providing strong evidence of asymmetric investor induced contagion, triggered by cross asset rebalancing. The critical role of the credit crisis is amplified, as the beginning of an important reassessment of emerging market currencies which lead to changes in the dependence structure, a revaluation and recalibration of their risk characteristics. By modelling tail risks we detect structural breaks and find patterns consistent with the domino effect. JEL Classification: C5, F31, F37, G01, G17.

The present paper sheds a new light on the notorious question in the evolutionary biology of why the modern species exhibit only the asexual and binary mating systems, with the clear dominance of the latter over the former. We present an in-depth study of the intertemporal propagation of the fundamental distributional properties of phenotypes in general polygenic multi-gender inheritance models with sex- and time-dependent heritability. We further analyze the implications of these models under thick-tailedness of traits' initial distributions. We obtain the results that demonstrate that, under an arbitrary multi-sex mating system with k genders, the Organism's switching to a more uniform mode of heritability leads to an increase in peakedness and concentration of traits with not extremely heavy-tailed initial distributions in its population in all the future periods. However, the decrease in the diversity of the parameters responsible for the different sexes' genetical contributions to the next period's offspring leads to an increase in concentration and peakedness of extremely long-tailed traits in all future generations. From these results it follows that switching to an inheritance system with greater diversity in heritability coeffcients and, thus, an increase in the number of genders under symmetric heritability, is advantageous in the case of extremely long-tailed traits that have negative effects on the population's fitness (say, human medical or behavioral disorders for which inheritance is significant). Such a switching or increase in the number of genders slows down or completely stops the intertemporal spread of the extremely thick-tailed negative traits in the population. On the other hand, a decrease in the number of genders in the symmetric multi-sex inheritance system and, more generally, switching to less diverse heritability parameters is advantageous in the case of not extremely thick-tailed positive traits (e.g., the trait of intelligence). Our theoretical results demonstrate that the intertemporal propagation of distributional properties of traits is, to a large extent, responsible for the dominance of the asexual and binary mating systems in nature. Namely, from the results obtained in the paper it follows that the switching between the asexual and binary inheritance mechanisms allows the population to achieve effectively a relatively fast decline (sharp concentration) of bad traits or a relatively quick spread (decrease of peakedness and concentration) of good traits, regardless of the distributional properties of the phenotypes in the initial period, in particular, regardless of the degree of heavy-tailedness of their initial densities. Furthermore, from our results it follows that, regardless of their initial distributional properties, the propagation of negative traits in a population with three or more genders can be prevented and the wide spread of positive phenotypes can be achieved immediately or in a relatively near future if the population switches to a mating system with only one or two genders. Given the high costs to species of developing and maintaining extra genders, this makes the asexual and binary inheritance mechanisms advantageous comparing to other mating systems.

Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that, generally, it is difficult to construct an appropriate risk measure for such distributions. We further analyze the limitations of diversification for heavy-tailed risks. We provide additional insight in two ways. First, we show that similar nondiversification results are valid for a large class of risks with bounded support, as long as the risks are concentrated on a sufficiently large interval. The required length of the support depends on the number of risks available and on the degree of heavy-tailedness. Second, we relate the value at risk approach to more general risk frameworks. We argue that in financial markets where the number of assets is limited compared with the (bounded) distributional support of the risks, unbounded heavy-tailed risks may provide a reasonable approximation. We suggest that this type of analysis may have a role in explaining various types of market failures in markets for assets with possibly large negative outcomes.

We develop a framework that allows one to model the optimal bundling problem of a multiproduct monopolist providing interrelated goods with an arbitrary degree of complementarity or substitutability. Characterizations of optimal bundling strategies are derived for the seller in the case of long-tailed valuations and tastes for the products. We show, in particular, that if goods provided in a Vickrey auction or any other revenue equivalent auction are substitutes and bidders' tastes for the objects are not extremely heavy-tailed, then the monopolist prefers separate provision of the products. However, if the goods are complements and consumers' tastes are extremely thick- tailed, then the seller prefers providing the products on a single auction. We also present results on consumers' preferences over bundled auctions in the case when their valuations exhibit heavy-tailedness. In addition, we obtain characterizations of optimal bundling strategies for a monopolist who provides complements or substitutes for profit maximizing prices to buyers with long-tailed tastes.

This paper develops a new unified approach to copula-based modeling and characterizations for time series and stochastic processes. We obtain complete characterizations of many time series dependence structures in terms of copulas corresponding to their finite-dimensional distributions. In particular, we focus on copula-based representations for Markov chains of arbitrary order, m-dependent and r-independent time series as well as martingales and conditionally symmetric processes. Our results provide new methods for modeling time series that have prescribed dependence structures such as, for instance, higher order Markov processes as well as non-Markovian processes that nevertheless satisfy Chapman-Kolmogorov stochastic equations. We also focus on the construction and analysis of new classes of copulas that have flexibility to combine many different dependence properties for time series. Among other results, we present a study of new classes of copulas based on expansions by linear functions (Eyraud-Farlie-Gumbel-Mongenstern copulas), power functions (power copulas) and Fourier polynomials (Fourier copulas) and introduce methods for modeling time series using these classes of dependence functions. We also focus on the study of weak convergence of empirical copula processes in the time series context and obtain new results on asymptotic gaussianity of such processes or a wide class of beta-mixing sequences.

The present paper develops a new unified approach to the analysis of efficiency, peakedness and majorization properties of linear estimators. It further studies the robustness of these properties to heavy-tailedness assumptions. The main results show that peakedness and majorization phenomena for random samples from log-concavely distributed populations established in the seminal work by Proschan (1965) continue to hold for not extremely thick-tailed distributions. However, these phenomena are reversed in the case of populations with extremely heavy-tailed densities. Among other results, we show that the sample mean is the best linear unbiased estimator of the population mean for not extremely heavy-tailed populations in the sense of its peakedness properties. Moreover, in such a case, the sample mean exhibits the important property of monotone consistency and, thus, an increase in the sample size always improves its performance. However, as we demonstrate, effciency of the sample mean in the sense of its peakedness decreases with the sample size if the sample mean is used to estimate the population center under extreme thick-tailedness. We also provide applications of the main effciency and majorization comparison results in the study of concentration inequalities for linear estimators as well as their extensions to the case of wide classes of dependent data. The main results obtained in the paper provide the basis for the analysis of many problems in a number of other areas, in addition to econometrics and statistics, and, in particular, have applications in the study of robustness of model of firm growth for firms that can invest into information about their markets, value at risk analysis, optimal strategies for a multiproduct monopolist as well that of inheritance models in mathematical evolutionary theory.