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The aim of this paper is to introduce a new stochastic order based on the residual lifetimes of two nonnegative dependent random variables and the stochastic precedence order. We develop some characterizations and preservation properties of this stochastic order. In addition, we study some of its reliability properties and its relation with other existing stochastic orders. One of the possible applications in reliability theory has also been discussed.

The study proposes to include the financial analysis (FA) in optimal portfolio selection. The role of FA in investment decisions is well recognized. While comparing two stocks on FA of their companies it is important to have both drawn from the same sector of economy. This reason motivated us to propose a sectoral portfolio optimization (SPO) which, instead of looking to optimize among all stocks together, focuses on optimizing stocks within each sector on the basis of FA. These stocks are then pooled together and an optimal portfolio is formed from them with their FA weights and mean returns. In context of FA, the four financial ratios included in present study are return on asset (profitable ratio), debt-assets ratio (solvency ratio), current ratio (liquidity ratio), and price-to-earning ratio (valuation ratio). The risk in a portfolio is quantified using the second order stochastic dominance and to this effect constraints are added in the selection process to generate optimal portfolios for rational risk averse investors. The performance of the optimal portfolios from the proposed model is tested against the portfolios from the traditional second order stochastic dominance model [named (SSDP) in this work], the benchmark index and four 5-star rated mutual funds of India from diversified equity. The out-of-sample analysis is carried on mean returns, Sharpe ratio, Sortino ratio, and also their ability to dominate the benchmark index in almost second order stochastic dominance sense over the tolerable violation regions. The stock price data for the period April 2004 to November 2014 of S&P BSE 500 index is used for testing the models. The optimal portfolios generated from the SPO perform better than the portfolios generated from the (SSDP), the benchmark index and the MFs, indicating effectiveness of FA in SPO framework.

Strassen's classical martingale coupling theorem states that two random vectors are ordered in the convex (resp. increasing convex) stochastic order if and only if they admit a martingale (resp. submartingale) coupling. By analysing topological properties of spaces of probability measures equipped with a Wasserstein metric and applying a measurable selection theorem, we prove a conditional version of this result for random vectors conditioned on a random element taking values in a general measurable space. We provide an analogue of the conditional martingale coupling theorem in the language of probability kernels, and discuss how it can be applied in the analysis of pseudo-marginal Markov chain Monte Carlo algorithms. We also illustrate how our results imply the existence of a measurable minimiser in the context of martingale optimal transport.

Farinelli and Tibiletti (F–T) ratio, a general risk-reward performance measurement ratio, is popular due to its simplicity and yet generality that both Omega ratio and upside potential ratio are its special cases. The F–T ratios are ratios of average gains to average losses with respect to a target, each raised by a power index, p and q. In this paper, we establish the consistency of F–T ratios with any nonnegative values p and q with respect to first-order stochastic dominance. Second-order stochastic dominance does not lead to F–T ratios with any nonnegative values p and q, but can lead to F–T dominance with any p < 1 and q ≥ 1. Furthermore, higher-order stochastic dominance (n ≥ 3) leads to F–T dominance with any p < 1 and q ≥ n-1. We also find that when the variables being compared belong to the same locationscale family or the same linear combination of location-scale families, we can get the necessary relationship between the stochastic dominance with the F–T ratio after imposing some conditions on the means. There are many advantages of using the F–T ratio over other measures, and academics and practitioners can benefit by using the theory we developed in this paper. For example, the F–T ratio can be used to detect whether there is any arbitrage opportunity in the market, whether there is any anomaly in the market, whether the market is efficient, whether there is any preference of any higher-order moment in the market, and whether there is any higherorder stochastic dominance in the market. Thus, our findings enable academics and practitioners to draw better decision in their analysis.

The orthant convex and concave orders have been studied in the literature as extensions of univariate variability orders. In this paper, new results are proposed for bivariate orthant convex-type orders between vectors. In particular, we prove that these orders cannot be considered as dependence orders since they fail to verify several desirable properties that any positive dependence order should satisfy. Among other results, the relationships between these orders under certain transformations are presented, as well as that the orthant convex orders between bivariate random vectors with the same means are sufficient conditions to order the corresponding covariances. We also show that establishing the upper orthant convex or lower orthant concave orders between two vectors in the same Fréchet class is not equivalent to establishing these orders between the corresponding copulas except when marginals are uniform distributions. Several examples related with concordance measures, such as Kendall’s tau and Spearman’s rho, are also given, as are results on mixture models.

A key premise underlying most of the economic literature is that rational decision-makers will choose dominant strategies over dominated alternatives. However, prior literature in various disciplines including business, psychology, and economics document a series of phenomena associated with violations of the dominance principle in decision-making. In this comprehensive review, we discuss conditions under which people violate the dominance principle in decision-making. When presenting violations of dominance in empirical and experimental studies, we differentiate between absolute, statewise, and stochastic (first- and second-order) violations of dominance. Furthermore, we categorize the literature by the leading causes for dominance violations: framing, reference points, certainty effects, bounded rationality, and emotional responses.

We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence (SP) order that is defined for two random variables to the case n > 2. All conventional stochastic orders are transitive, whereas the SP order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.

Recently, additive hazards (AH) model has been introduced in the literature for modeling and analyzing failure time data. In this paper, a new extended additive hazards model is introduced and analyzed and some properties of this model and some further properties of AH model related to reliability analysis are investigated. Under some appropriate assumptions, it is shown that the mixing and the overall variables in the model admit some kinds of positive (negative) dependence structures and closure properties of the model with respect to some conditional stochastic orderings and aging properties are studied.

We study various partially ordered spaces of probability measures and we determine which of them are lattices. This has important consequences for optimization problems with stochastic dominance constraints. In particular we show that the space of probability measures on $\\mathbb{R}$ is a lattice under most of the known partial orders, whereas the space of probability measures on $\\mathbb{R}^d$ typically is not. Nevertheless, some subsets of this space, defined by imposing strong conditions on the dependence structure of the measures, are lattices.

We consider convex optimization problems with $k$th order stochastic dominance constraints for $k\\ge 2$. We discuss distances of random variables that are relevant for the dominance relation and establish quantitative stability results for optimal values and solution sets of the optimization problems in terms of a suitably selected probability metrics. Moreover, we provide conditions ensuring Hadamard directional differentiablity of the optimal value function. We introduce the notion of a shadow utility, which determines the changes of the optimal value when the underlying random variables are perturbed. Finally, we derive a limit theorem for the optimal values of empirical (Monte Carlo, sample average) approximations of dominance constrained optimization models. [PUBLICATION ABSTRACT]