Correlated equilibrium in a nutshell

We analyze the concept of correlated equilibrium in the framework of two-player two-strategy games. This simple framework makes it possible to clearly demonstrate the characteristic features of this concept. We develop an intuitive and easily memorizable test for equilibrium conditions and provide a complete classification of symmetric correlated equilibria in symmetric games.     

The changing nature of rurality and rural studies in Russia

This paper seeks to outline different strands of the reconfiguration of the social and spatial perspectives on the countryside in Russia in the last 20 years. The country's transition implied changes in the production of knowledge, including the re-examination of research topics and bringing new theories into rural studies. The article strives to develop a theoretically informed critique of the recent studies, specifically addressing the changing vision of rurality. Taking as a starting point traditional concerns in rural discourses, i.e. the ways rurality have been traditionally studied in Russia, this paper seeks to identify what rural studies might gain and lose from the shift in academic research. Critics have focused on the problems of bringing together past and recent trajectories in rural research, concentrating on the power of construction of particular rural discourses in different environments. The reconstruction of changing rural discourses aims to provide an interpretative framework for understanding the ways various rural images and policy concepts are implicated in the construction of the Russian countryside.     

The Long-Term Effect of the Timing of Fertility Decline on Population Size

Existing long-range population projections imply that the timing of the fertility transition has a relatively unimportant effect on long-term population size when compared with the impact of the level at which fertility is assumed eventually to stabilize. However, this note shows that the effect of the timing of fertility decline is a function of the eventual fertility rate: the lower the eventual fertility rate, the greater the effect of the timing of the transition becomes. This finding has important implications for projection methodology, as well as for policies related to the consequences of long-term levels of population size.     

Analytical and numerical studies on the second-order asymptotic expansion method for European option pricing under two-factor stochastic volatilities

The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013, Chiarella and Ziveyi considered Christoffersen’s ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast (for example daily) and slow (for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first- and second-order asymptotic expansion formulas.     

The uncertain timing of reaching 8 billion, peak world population, and other demographic milestones

We present new probabilistic forecasts of the timing of the world's population reaching 8 billion, the world's peak population, and the date at which one-third or more of the world's population would be 60+ years old. The timing of these milestones, as well as the timing of the Day of 7 Billion, is uncertain. We compute that the 60 percent prediction interval for the Day of 8 Billion is between 2024 and 2033. Our figures show that there is around a 60 percent chance that one-third of the world's population would be 60+ years old in 2100. In the UN 2010 medium variant, that proportion never reaches one-third. As in our past forecasts (Lutz et al. 2001, 2008), we find the chance that the world's population will peak in this century to be around 84 percent and the timing of that peak to be highly uncertain. Focal days, like the Day of 7 Billion, play a role in raising public awareness of population issues, but they give a false sense of the certainty of our knowledge. The uncertainty of the timing of demographic milestones is not a constant of nature. Understanding the true extent of our demographic uncertainty can help motivate governments and other agencies to make the investments necessary to reduce it.     

Are We Overly Dependent on Conventional Dependency Ratios?

The dependency ratio and its components have had a long and productive life. Here we show that they are no longer the most accurate way of measuring important aspects of population aging. We present ratios related to employment, standardized workers and consumers, health care costs, pension costs, and who is old. These ratios are based either on new data or on new approaches to the study of population aging and are all available on the internet. We compare forecasts of those ratios with forecasts of the dependency ratio, both based on the same UN population data. In all cases, we find that the dependency ratio and the old‐age dependency ratio are poor approximations to the more up‐to‐date ratios. There is little need to use the dependency ratio. More accurate measures are readily available.     

Sample size calculation for the Power Model for dose proportionality studies

There are several approaches to assess or demonstrate pharmacokinetic dose proportionality. One statistical method is the traditional ANOVA model, where dose proportionality is evaluated using the bioequivalence limits. A more informative method is the mixed effects Power Model, where dose proportionality is assessed using a decision rule for the estimated slope. Here we propose analytical derivations of sample sizes for various designs (including crossover, incomplete block and parallel group designs) to be analysed according to the Power Model.     

Steepest descent algorithms in a space of measures

The paper describes descent type algorithms suitable for solving optimisation problems for functionals that depend on measures. We mention several examples of such problems that appear in optimal design, cluster analysis and optimisation of spatial distribution of coverage processes.     

The Civilizational Measure “Krymnash” [“Crimea Is Ours”]

The article discusses the notion of “Russian Civilization,” and the ways in which it has been challenged in the last two centuries. Central to the discussion is the question of the extent to which there is a shared Slavic set of cultural beliefs, and the degree to which Russian/Slavic civilization is prepared to move from a state-centered to an individual-centered set of values.