Order Stochastic Dominance Research Articles

A Two-Parameter Family of Socio-Economic Health Inequality Indices: Accounting for Risk and Inequality Aversions

This paper proposes a two-parameter family of socio-economic health inequality indices. First, these indices allow a Boolean risk factor to be associated to other health dimensions. Second, multidimensional health distributions can be compared thanks to a stochastic dominance rule, which includes the attitude of the social planner with respect to the risk factor (risk neutrality, risk aversion and extreme risk aversion). Third, each order of stochastic dominance is also associated to the intensity of possible health transfers occurring between individuals, that is, the degree of inequality aversion of the social planner. This approach is a multidimensional extension of Yitzhaki's Gini indices accounting simultaneously for risk and redistribution.

Cone distribution functions and quantiles for multivariate random variables

Set-valued quantiles for multivariate distributions with respect to a general convex cone are introduced which are based on a family of (univariate) distribution functions rather than on the joint distribution function. It is shown that these quantiles enjoy basically all the properties of univariate quantile functions. Relationships to families of univariate quantile functions and to depth functions are discussed. Finally, a corresponding Value-at-Risk for multivariate random variables as well as a stochastic (dominance) order based on quantiles are introduced via the set-valued approach.

Dynamics of Multidimensional Poverty and Uni-dimensional Income Poverty: An Evidence of Stability Analysis from China

In this paper, we construct an illustrative multidimensional poverty index for China and compare it with income poverty using the panel data from multiple waves of the China Health and Nutrition Survey. We use first order stochastic dominance method and regression analysis to test the stability of multidimensional poverty measures and probe the often-observed mis-match between multidimensional measures and income measures. We find as expected that China’s multidimensional poverty is significantly higher in rural areas and in the less developed western provinces. But relative to the income poverty, the multidimensional poverty is less volatile. Also, the ranking of provinces by income and multidimensional poverty varies. The multidimensional poverty measures are somewhat sensitive to the large change of weight, but if we control the indicators’ weight, then the multidimensional poverty measures are stable to a change of indicators.

SSD Efficiency at Multiple Data Frequencies: Application on the OECD Countries

The second order stochastic dominance (SSD) has become exceedingly popular in recent years,due to its ability to determine the dominance of one asset over another for all risk-averse investorswithout a strict requirement in asset distribution. In this study, 33 OECD country indexes and theirenriched set of assets, which consists of some combinations of these indexes, are investigatedand compared between 2007 and 2015 by utilizing pairwise SSD comparisons, with different datafrequencies, such as daily, weekly, monthly and quarterly. This paper contributes to the literaturein three points: Firstly, a serious portion of the best performing OECD countries has the lowest GDP(PPP) per capita level. Secondly, the SSD efficient set depends on data frequency. Thirdly, whenthe data frequency is lowered, the difference between two SSD pairwise efficiency tests decreases.

Risk-Tabanlı VZA ve Stokastik Baskınlık Kriteri ile OECD Üyelerinin Hisse Senedi Endekslerinin Etkinliği

A stock market index gives some illustrative information regarding the financial market. In this study, we are interested in stock indices efficiency of OECD member countries. We use Data Envelopment Analysis (DEA) methodology and Second Order Stochastic Dominance (SSD) Criteria as an efficiency metrics. DEA is a linear programming based technique for measuring the relative efficiency of homogenous decision making units by their input-output rates. In the Risk-Based DEA, traditional and modern risk measures are used as inputs of the model and the mean return as an output. We consider Conditional Value at Risk (CVaR) as a modern risk measure of financial asset returns. Another approach for the efficiency is Stochastic Dominance (SD) rule that takes into account the entire distribution of return, rather than the return distribution characteristics. There are several papers show that SSD constraints related to the CVaR constraints in an optimization model. Therefore, we compare Risk-Based DEA results with optimization problem with SSD constraints in the empirical study. We also test SSD efficiency of stock index pairs. The results are valuable for the asset managers who need to evaluate the performance of a stock index among others.

Fair solutions to the random assignment problem

We study the problem of assigning indivisible goods to individuals where each is to receive one good. To guarantee fairness in the absence of monetary compensation, we consider random assignments that individuals evaluate according to first order stochastic dominance (sd). In particular, we find that solutions which guarantee sd-no-envy (e.g. the Probabilistic Serial) are incompatible even with the weak sd-core from equal division. Solutions on the other hand that produce assignments in the strong sd-core from equal division (e.g. Hylland and Zeckhauser’s Walrasian Equilibria from Equal Incomes) are incompatible with the strong sd-equal-division-lower-bound. As an alternative, we present a solution, based on Walrasian equilibria, that is sd-efficient, in the weak sd-core from equal division, and satisfies the strong sd-equal-division-lower-bound.

ALM models based on second order stochastic dominance

We propose asset and liability management models in which the risk of underfunding is modelled based on the concept of stochastic dominance. Investment decisions are taken such that the distribution of the funding ratio, that is, the ratio of asset to liabilities, is non-dominated with respect to second order stochastic dominance. In addition, the funding ratio distribution is close in an optimal sense to a user-specified target distribution. Interesting results are obtained when the target distribution is degenerate; in this case, we can obtain equivalent risk minimisation models, with risk defined as expected shortfall or as worst case loss. As an application, we consider the financial planning problem of a defined benefit pension fund in Saudi Arabia.

Indexing gamble desirability by extending proportional stochastic dominance

We characterise two new orders of desirability of gambles (risky assets) that are natural extensions of the stochastic dominance order to complete orders, based on choosing optimal proportions of gambles. These orders are represented by indices, which we term the S index and the G index, that are characterised axiomatically and by wealth and utility uniform dominance concepts. The S index can be viewed as a generalised Sharpe ratio, and the G index can be used for maximising the growth path of a portfolio.

Extensions on Stochastic Dominance Efficiency Tests

We consider second, third, fourth and fifth order stochastic dominance (SSD, TSD, FOSD and FISD, respectively) as well as decreasing absolute risk aversion (DARA) stochastic dominance (DSD). For comparison with DSD we also consider stochastic dominance (ESD) based on CARA utility functions. Their relevance in practice arises from empirical evidence on individual preferences fitting to preference models underlying such stochastic dominance relations. Assuming a known, discrete and finite probability distribution we derive necessary and sufficient efficiency tests under the six types of stochastic dominance. Simple arguments yield well-known SSD and TSD efficiency tests which are subsequently used to develop new FOSD, FISD, DSD and ESD efficiency tests. We provide numerical demonstration using stock market data of the US.

New Development on the Third Order Stochastic Dominance for Risk-Averse and Risk-Seeking Investors with Application in Risk Management

This paper develops new financial theory to link the third order stochastic dominance for risk-averse and risk-seeking investors and provide illustration of application in risk management. We present some interesting new properties of third order stochastic dominance (TSD) for risk-averse and risk-seeking investors. We show that the means of the assets being compared should be included in the definition of TSD for both investor types. We also derive the conditions on the variance order of two assets with equal means for both investor types and extend the second order SD (SSD) reversal result of Levy and Levy (2002) to TSD. We apply our results to analyze the investment behaviors on traditional stocks and internet stocks for both risk averters and risk seekers.

Time Will Tell: Recovering Preferences When Choices are Noisy

The ability to uncover preferences from choices is fundamental for both positive economics and welfare analysis. Overwhelming evidence shows that choice is stochastic, which has given rise to random utility models as the dominant paradigm in applied microeconomics. However, as is well known, it is not possible to infer the structure of preferences in the absence of assumptions on the structure of noise. This makes it impossible to empirically test the structure of noise independently from the structure of preferences. Here, we show that the difficulty can be bypassed if data sets are enlarged to include response times. A simple condition on response time distributions (a weaker version of first order stochastic dominance) ensures that choices reveal preferences without assumptions on the structure of utility noise. Sharper results are obtained if the analysis is restricted to specific classes of models. Under symmetric noise, response times allow to uncover preferences for choice pairs outside the data set, and if noise is Fechnerian, even choice probabilities can be forecast out of sample. We conclude by showing that standard random utility models from economics and standard drift-diffusion models from psychology necessarily generate data sets fulfilling our sufficient condition on response time distributions.

Dynamics of Multidimensional Poverty and Uni‐dimensional Income Poverty: An Evidence of Stability Analysis from China

In this paper, we construct an illustrative multidimensional poverty index for China and compare it with income poverty using the panel data from multiple waves of the China Health and Nutrition Survey. We use first order stochastic dominance method and regression analysis to test the stability of multidimensional poverty measures and probe the often-observed mis-match between multidimensional measures and income measures. We find as expected that China’s multidimensional poverty is significantly higher in rural areas and in the less developed western provinces. But relative to the income poverty, the multidimensional poverty is less volatile. Also, the ranking of provinces by income and multidimensional poverty varies. The multidimensional poverty measures are somewhat sensitive to the large change of weight, but if we control the indicators’ weight, then the multidimensional poverty measures are stable to a change of indicators.

Higher-degree Stochastic Dominance Orders: Equivalence of Two Alternative Systems of Inequalities

Higher-degree Stochastic Dominance Orders: Equivalence of Two Alternative Systems of Inequalities

Precautionary saving in a Markovian earnings environment

Under what conditions does an increase in the future income risk (in the sense of second order stochastic dominance) result in an increase in savings? This paper establishes a novel sufficient condition for the case in which income follows a Markov process. The sufficient condition applies to a broad class of preferences and processes that are often adopted in the applied literature.

Bayesian inference for health inequality and welfare using qualitative data

We show how to use Bayesian inference to compare two ordinal categorical distributions commonly occurring with data on self-reported health status. Procedures for computing probabilities for first and second order stochastic dominance and S-dominance are described, along with methodology for obtaining posterior densities for health inequality indexes. The techniques are applied to four years of data on Australian self-reported health status.

A case of sustainable intensification: Stochastic farm budget optimization considering internal economic benefits of biogas production in organic agriculture

Organic agriculture is often criticized for its lower productivity compared to conventional farming, while biogas production on organic farms is confronted with many structural constraints additionally impeding its profitability. However, integrated anaerobic digestion seems to induce multiple benefits for the respective organic farm system, such as reduced environmental impacts, improved nutrient efficiency, and stabilized or increased yields. In order to measure these effects within entire farm systems, systemic evaluation approaches are needed. Consequently, in this study we modelled twelve different livestock-keeping (LS) and stockless (noLS) organic farm prototypes comprising of arable farming, dairy cattle, grassland, and biogas production in a farm system assessment. The aim was to evaluate the impact of integrated anaerobic digestion (+AD) on agronomic, economic, and risk aspects by applying stochastic optimization. While the absolute amount of readily available nitrogen as well as cash crop yields increase for both LS +AD and noLS +AD farm models, especially noLS farm types benefit from the novel availability of a mobile nitrogen (N) fertilizer (biogas digestate) to meet cash crop N demands. Integrated AD may increase profitability of arable farming and reduce its risk potential by displaying first order stochastic dominance. In addition, this diversification strategy may reduce the overall production risk of organic farms. By providing renewable energy as well as increasing food outputs and economic stability, the integration of AD in organic farms may serve as an example for the often postulated aim of a sustainable or eco-functional intensification of organic agricultural systems to face the challenge of productivity increases.

Indirect exports and wholesalers: Evidence from interfirm transaction network data

A substantial fraction of international trade is facilitated by wholesalers, who enable manufacturers to indirectly export their products to foreign markets. Using large-scale Japanese interfirm transaction network data, this paper investigates the features of both direct and indirect exporters as well as international wholesalers. As predicted by a simple Melitz-type trade model with indirect export alternative, the sorting pattern is confirmed in our data, and the distributions of sales and labor productivity are ordered for direct, indirect, and non-exporters in terms of first order stochastic dominance. Multinomial logit analysis is also consistent with the model, which assumes lower fixed cost and higher marginal cost for indirect exporters compared to direct exporters. We also find that the number of suppliers raises the probability of direct exporting implying a cost sharing mechanism of firms with more suppliers. On the other hand, the number of customers raises the probability of exporting in general (both indirect and direct) implying a higher product appeal and broader demand base for firms who have more customers.

Portfolio analysis with second order stochastic dominance by the perspective of capital structure: an implementation on BIST-100 index

Purpose- The aim of this paper is to observe whether generating a portfolio having return more than index by investigating the return performance of index’s stocks and capital structure of firms in index in a certain period. The second aim of this paper is to provide portfolio diversification by using the method of this study. In this paper, firms and stocks on BIST-100 index are referenced for empirical study. Method- Stocks are chosen from BIST-100 index with regard to certain capital structure of firms in stocks, and second orderly stochastic dominance test is implemented on these stocks. Dominant stocks are defined to generate a portfolio after stochastic test and this portfolio’s return performance is compared to the index’-s return. Findings- The portfolio, whose stocks are filtered by a certain capital structure and then chosen by second orderly stochastic dominance test, has return performance better than index’s return. Conclusion- This paper is indicating that second orderly stochastic dominance method and capital structure is an important investigation to generate a portfolio having higher returns more than index’s.

Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints

The portfolio optimization problem is the central problem of modern economics and decision theory; there is the Mean-Variance Model and Stochastic Dominance Model for solving this problem. In this paper, based on the second order stochastic dominance constraints, we propose the improved biogeography-based optimization algorithm to optimize the portfolio, which we called ε BBO. In order to test the computing power of ε BBO, we carry out two numerical experiments in several kinds of constraints. In experiment 1, comparing the Stochastic Approximation (SA) method with the Level Function (LF) algorithm and Genetic Algorithm (GA), we get a similar optimal solution by ε BBO in [ 0 , 0 . 6 ] and [ 0 , 1 ] constraints with the return of 1.174% and 1.178%. In [ - 1 , 2 ] constraint, we get the optimal return of 1.3043% by ε BBO, while the return of SA and LF is 1.23% and 1.26%. In experiment 2, we get the optimal return of 0.1325% and 0.3197% by ε BBO in [ 0 , 0 . 1 ] and [ - 0 . 05 , 0 . 15 ] constraints. As a comparison, the return of FTSE100 Index portfolio is 0.0937%. The results prove that ε BBO algorithm has great potential in the field of financial decision-making, it also shows that ε BBO algorithm has a better performance in optimization problem.

How risky is a random process?

The riskiness of random processes is compared by (a) employing a decision theoretic equivalence between processes and lotteries on path-spaces to identify the riskiness of the former with that of the latter, and (b) using the theory of comparative riskiness of lotteries over vector spaces to compare the riskiness of lotteries on a given path-space. We derive the equivalence used in step (a) and contribute a new criterion to the theory applied in step (b). The validity of the new criterion, which applies second order stochastic dominance to utility distributions, is established by showing its equivalence to the benchmark decision theoretic criterion when comparing the riskiness of lotteries over any vector space. We demonstrate the theory’s tractability via diverse economic applications.