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To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

The methodology is based on an n‐th order expansion (perturbation) for input random parameters and state functions around their expected value to recover probabilistic moments of the response. A finite element formulation permits stochastic simulations on irregular meshes for practical applications.

The methodology permits approximation of expected values and covariances of quantities such as the fluid pressure and flow velocity using both symbolic and discrete FEM computations. It is applied to inviscid irrotational flow, Poiseulle flow and viscous Couette flow with randomly perturbed boundary conditions, channel height and fluid viscosity to illustrate the scheme.

The focus of the present work is on the basic concepts as a foundation for extension to engineering applications. The formulation for the viscous incompressible problem can be implemented by extending a 3D viscous primitive variable finite element code as outlined in the paper. For the case where the physical parameters are temperature dependent this will necessitate solution of highly non‐linear stochastic differential equations.

Techniques presented here provide an efficient approach for numerical analyses of heat transfer and fluid flow problems, where input design parameters and/or physical quantities may have small random fluctuations. Such an analysis provides a basis for stochastic computational reliability analysis.

The mathematical formulation and computational implementation of the generalized perturbation‐based stochastic finite element method (SFEM) is the main contribution of the paper.

Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

With suitable optimization criteria, hybrid models have proven to be efficient for preparing portfolios in capital markets of developed countries. This study adapts and investigates these methods for a developing country, thus providing a novel approach to the application of banking and finance. Our specific objectives are to employ a stochastic dominance criterion to evaluate the performances of over-the-counter (OTC) companies in a developing country and to analyze them with a hybrid model involving particle swarm optimization and artificial neural networks.

In order to achieve these aims, the authors conduct a case study of OTC companies in Iran. Weekly and daily returns of 36 companies listed in this market are calculated for one year during 2014–2015. The hybrid model is particularly interesting, and the results of the study identify first-, second- and third-order stochastic dominances among these companies. The study’s chosen model uses the best performing combination of activation functions in our analysis, corresponding to TPT, where T represents hyperbolic tangent transfers and P represents linear transfers.

Our portfolios are based on the shares of companies ranked with respect to the stochastic dominance criterion. Considering the minimum and maximum numbers of shares to be 2 and 10 for each portfolio, an eight-share portfolio is determined to be optimal. Compared with the index of Iran OTC during the research period of this study, our selected portfolio achieves a significantly better performance. Moreover, the methods used in this analysis are shown to be as efficient as they were in the capital markets of developed countries.

The problem of optimizing investment portfolios has to allow for correlations among returns from the financial maintenance period under consideration if an asymmetric distribution of returns exists (Babaei et al., 2015). Therefore, it is desirable to select an appropriate criterion in order to prepare an optimal portfolio and prioritize investment options. Although a back propagation technique is very popular in artificial neural (ANN) training, it is time-consuming to train a network in this way, and other methods such as particle swarm optimization (PSO) should be considered instead. In the hybrid combination of PSO and ANN, it is not the structure of a neural network that changes. Rather, the weighting method and the training technique chosen for the network are the important aspects, and these relate to PSO, so the only role ANN plays in this process is to reduce the errors.

The hybrid model combining ANN and PSO is seen to be considerably successful for generating optimal results and appropriate activation functions. These results are consistent with the theoretical findings of Das et al. (2013) and an application of the simple PSO in a study conducted by Pederson and Chipperfield (2010). Our research results also confirm the efficiency of stochastic dominance criteria as noted in the studies conducted by Roman et al. (2013), ANN as in a study carried out by Kristijanpoller et al. (2014) and PSO as in studies conducted by Liu et al. (2015) and Deng et al. (2012). These studies were carried out in the capital markets of developed countries, whereas the authors’ analysis relates to a developing country.

The authors deduce that the tools and methods whose efficiency was proven in the capital markets of developed countries also apply to, and demonstrate efficiency in, two novel applications of portfolio optimization within developing countries. The first of these is gaining familiarity with the theory and practice of these research tools and the methods that enrich financial knowledge of investors in developing countries. The second of these is the application of tools and methods identified by investors in the capital markets of developing countries, which enables optimal allocation of financial resources and growth of the markets. The authors expect that these findings will contribute to improving the economies of developing countries and thus help with economic development and facilitation of improving trends.

Recently, star variables and the post-crisis nature of cyclical fluctuations have attracted a great deal of interest. In this chapter, the authors investigate different methods of assessing business cycles (BCs) for the European Union in general and the euro area in particular. First, the authors conduct a Monte Carlo (MC) experiment using a broad spectrum of univariate trend-cycle decomposition methods. The simulation aims to examine the ability of the analysed methods to find the observed simulated cycle with structural properties similar to actual macroeconomic data. For the simulation, the authors used the structural model’s parameters calibrated to the euro area’s real gross domestic product (GDP) and unemployment rate. The simulation outcomes indicate the sufficient composition of the suite of models (SoM) consisting of popular Hodrick–Prescott, Christiano–Fitzgerald and structural trend-cycle-seasonal filters, then used for the real application. The authors find that: (i) there is a high level of model uncertainty in comparing the estimates; (ii) growth rate (acceleration) cycles have often the worst performances, but they could be useful as early-warning predictors of turning points in growth and BCs; and (iii) the best-performing MC approaches provide a reasonable combination as the SoM. When swings last less time and/or are smaller, it is easier to pick a good alternative method to the suite to capture the BC for real GDP. Second, the authors estimate the BCs for real GDP and unemployment data varying from 1995Q1 to 2020Q4 (GDP) or 2020Q3 (unemployment), ending up with 28 cycles per country. This analysis also confirms that the BCs of euro area members are quite synchronized with the aggregate euro area. Some major differences can be found, however, especially in the case of periphery and new member states, with the latter improving in terms of coherency after the global financial crisis. The German cycles are among the cyclical movements least synchronized with the aggregate euro area.

This study analyzes the effect of ambiguity aversion on precautionary effort under a two period model when background risk like income risk is added to loss. Precautionary effort only affects the probability of loss occurrence. The sufficient conditions under which a risk averse and ambiguity averse individual makes more effort than a risk averse and ambiguity neutral one are as follows. First, the distribution of background risk changes in type of first order stochastic dominance. Second, the distribution of background risk changes in type of second order stochastic dominance and the utility function shows prudence. In both cases, AAA (absolute ambiguity aversion) should not increase. That is, AAA denotes DAAA (Decreasing Absolute Ambiguity Aversion) or CAAA (Constant Absolute Ambiguity Aversion). The effect of AAA is not observed in the existing literatures which assume a one-period model. In a one period model, the effect of AAA on precautionary effort of a long term may have ignored. Lastly, precautionary effort increases if and only if AAA is not increasing in cases when the background risk follows binary distribution or an individual is risk neutral and ambiguity averse.

To promote the development of renewable energy, the Chinese Government adopts the policy of Feed-in Tariff and subsidy. However, the high purchase price and the intermittence limit the development of renewable energy source electricity (RES-E). The purpose of this paper is to discuss the pricing strategy for system operators to stimulate the development of the RES-E industry under the scenario of uncertain supply and demand.

The authors establish a two-echelon supply chain investment model led by a power grid operator considering the uncertainties in both demand and supply, and study the impact of the power purchase price designed by a system operator using Stackelberg’s model.

There is an optimal capacity for RES-E generators, that is, independent of the market demand. Besides, the optimal order of grid operators is independent of the uncertain RES-E supply and the purchase price of fossil fuel. By properly setting the purchase prices, the system operator can stimulate the capacity investment in renewable energy. Finally, increasing the punishment in power shortage can stimulate the capacity investment in RES-E under certain conditions.

The result of this paper can mitigate the phenomenon of power abandonment in the RES-E industry and promote the grid integration of RES-E.

Both uncertain demand and supply are considered in this paper. A heuristic algorithm is provided to compute the optimal purchase price combination.

The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented.

First, Glaser’s functions of mixture and its components for weighted distributions in different scenarios are computed. Then by them the likelihood ratio order is investigated between mixture and its components.

The authors find conditions for weight functions under which the mixture random variable is between of its components in likelihood ratio order.

Results are obtained for weight function in general. It is well known that the some special weights are order statistics, up and down records, hazard rate, reversed hazard rate, moment generating function, etc. So, the results are valid for all of them.

This paper aims to compare two groups of stocks to analyze the efficiency of an ethical portfolio in comparison with a conventional portfolio.

Efficiency test by second-order stochastic dominance (SSD) approach is applied on two groups, which consist of 12 stocks. Ethical portfolio is chosen from the stocks complying with the participation banking rules. Conventional portfolio is selected from Borsa Istanbul (BIST) with choosing the corresponding stocks for each ethical stock according to the sector and market capitalization. All the stocks of both groups are pairwise SSD compared.

Both groups of 12 stocks are inefficient portfolios; however, a group of 7 stocks constitute an efficient ethical portfolio with the total weight of 50.82 per cent among the set of 12 ethical stocks. On the other hand, a group of 6 stocks constitute an efficient conventional portfolio, with the total weight of 45.16 per cent among the set of 12 conventional stocks. By pairwise SSD comparison of corresponding stocks from both groups, despite none of the conventional stocks dominate ethical stocks, four ethical stocks dominated the conventional ones.

Back-testing and comparison with benchmark BIST 100 Index have been done for the selected portfolios. According to back-testing results, groups of SSD efficient stocks outperformed the groups, from which they were selected. Furthermore, both SSD efficient portfolios have higher returns than benchmark index, BIST 100.

The purpose of this study is to examine the impact of thin trading on the day‐of‐the‐week effect in the emerging equity markets of the United Arab Emirates (UAE). Researchers have stated that emerging markets are typically characterized by low liquidity, thin trading and possibly less well‐informed investors with access to unreliable information and considerable volatility. It is well known that thin trading can affect the results of empirical studies on patterns of equity markets by introducing a serious bias into the results.

This study applies a stochastic dominance approach to detect the day‐of‐the‐week effect. The reason for utilizing this approach is that the parametric tests are not strictly appropriate for assets with non‐normally distributed returns. In fact, stochastic dominance is a useful tool for making comparisons among distributions without relying on parametric assumptions.

The findings indicate that there is day‐of‐the‐week effect in published daily prices, while daily effect vanishes when data are corrected to remove any measurement bias arising from thin trading. The stochastic dominance results show that the day‐of‐the‐week effect in the UAE equity markets is not present when we correct raw data for thin and infrequent trading.

There has been no research in the literature testing the day‐of‐the‐week effect on the emerging financial markets in the UAE. The study provides empirical evidence on their degree of market efficiency. If the day‐of‐the‐week effect exists, this means that the Abu Dhabi Securities Markets and the Dubai Financial Markets are inefficient. These results will help investors to develop a good investment strategy