Narrow Results

This paper applies stochastic dominance techniques for income distribution analysis and develops tests of richness and poorness to achieve more accurate characterizations of relative welfare in populations than was previously possible. Results from our empirical application, using Hong Kong data, are consistent with predictions of the life-cycle theory of income and savings. Among other things, we find high concentrations of poor individuals among the younger cohorts, and at the same time, there are high concentrations of rich individuals amongst the oldest cohorts. Our results help to explain Hong Kong’s persistently high levels of income inequality in the population.

We discuss the use of the ordered weighted averaging (OWA) operator in multi-criteria decision problems as a means of aggregating the individual criteria satisfactions. We emphasize the need for ordering the arguments, the criteria satisfactions, when using the OWA operator. We consider the situation where the criteria satisfactions have some uncertainty, are finite probability distributions and note the requirement of having to order probability distributions. We introduce the idea of using pairwise stochastic dominance to provide the necessary ordering relationship over the probability distributions. We note that while this approach is appropriate, it is often not possible, since the presence of a stochastic dominance relationship between all pairs of probability distributions is not always the case, the relationship is not complete. To circumvent this problem we introduce an approach called the probabilistic exceedance method (PEM), which allows us to provide a surrogate for the OWA aggregation of probability distributions that doesn't require a linear ordering over the probability distributions. We look at this in both the cases in which the criteria have equal and unequal importances.

Complex systems are subject to failure with increased use and degradation. The risk process is the stochastic dynamic process of system failures and their severities. This paper considers aggregate risk measures for the risk process of complex systems in the context of stochastic ordering. The aggregation follows from the accumulation of losses from a series of failure events. The emphasis is on second-order risk measures which account for risk aversion as defined by concave utilities. A second-order measure termed the adjusted risk priority number (ARPN) is presented. The measure is constructed from well-known statistics: rate of failures, average severity of failures, and the Gini Index for severity of failures. The ARPN is contrasted with the traditional risk priority number (RPN) defined by the rate and average severity. The computation and use of the measures is illustrated with a spectrum of failure data from commercial aircraft in the USA.

We consider a new approach towards stochastic dominance rules which allows measuring the degree of domination or violation of a given stochastic order and represents a way of describing stochastic orders in general. Examples are provided for the n-th order stochastic dominance and stochastic orders based on a popular risk measure. We demonstrate how the new approach can be used for construction of portfolios dominating a given benchmark prospect.

This paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We review classic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to a diversified set of assets and generalize them in the following aspects. First, we propose a linear programming SSD test that is more efficient than that of Post (2003). Secondly, we expand the SSD efficiency criteria developed by Dybvig and Ross (1982) onto the Third Order Stochastic Dominance and further to Decreasing Absolute and Increasing Relative Risk Aversion Stochastic Dominance. The efficient sets for those are finite unions of convex sets.

This paper derives the theoretical underpinnings behind the following observed empirical facts in credit risk modeling: The probability of default, the seniority, the thickness of the tranche, the debt cushion, and macroeconomic factors are the important determinants of the conditional probability density function of the recovery rate given default (RGD) of a firm’s debt and its tranches. In a portfolio of debt securities, the conditional probability density functions of the recovery rate given default of tranches have point probability masses near zero and one, and the expected value of the recovery rate given default increases as the seniority or debt cushion increases. The paper derives other results as well, such as the fact that the conditional probability distribution function associated with any senior tranche dominates that of any junior tranche by first-order. The standard deviation of the recovery rate given default of a senior security need not be greater than that of a junior security. It is proved that the expected value of the recovery rate given default need not increase as the proportional thickness of the tranche increases.

When one prospect is certain and the other uncertain, Cumulative Prospect Theory employs the certainty equivalent methodology to estimate Decision Weights (DW). However, DW may be different with two uncertain prospects. In this study, we neutralize the "certainty effect" and propose Stochastic Dominance (SD) to estimate DW for the first time with small probabilities, which is the raison d'être of the employment of DW. Using SD we provide ranges, rather than point estimates, of DW parameters that are consistent with all possible S-shape value functions. Comparing CE and SD implied DW, we find that DW are situation dependent: DW derived with one certain prospect are much different than those derived with two uncertain prospects.

Our paper contributes to the literature by developing the theory of the mean-variance (MV) rules for investors with reverse S-shaped utility. To do so, we first introduce the definition of the MV rule for investors with reverse S-shaped utility. We then set up the conjecture on the preference for different prospects by using the new MV rule that they could get a higher expected utility for the preferred asset under some conditions. Thereafter, we look for the conditions that the conjecture could hold and construct a theorem for this purpose by showing that when the negative (positive) parts of the assets follow one (another) type of location-scale family or the linear combination of location-scale families, then the preferences of the assets is the same as those by using an expected utility for the investors with reverse S-shaped utility. We then extend the theory by developing some properties of portfolio diversification by using the new MV rule. The theory developed in our paper enables academics and practitioners to apply the theory developed in this paper to analyze some important empirical issues and draw inferences on the preferences of investors with reverse S-shaped utility.

This paper investigates the dynamic links between renewable energy, commodities, and financial stock markets and analyzes the performance of renewable energy investment in an international portfolio diversification strategy across different financial market conditions. By using the dynamic spillover approach, the empirical results show that the renewable energy and oil markets are net emitters of shocks to stock markets. By applying the nonparametric stochastic dominance approach and comparing the optimal maximum Sharpe ratio (MSR) diversified portfolios, the results suggest that the renewable energy index can be a good substitute for traditional diversification, especially during tranquil periods.

Based upon Ritchken (1985), Levy (1985), Lo (1987), Zhang (1994), Jackwerth and Rubinstein (1996), and others, this chapter discusses the alternative method to determine option bound in terms of the first two moments of distribution. This approach includes stochastic dominance method and linear programming method, then we discuss semi-parametric method and non-parametric method for option-bound determination. Finally, we incorporate both skewness and kurtosis explicitly through extending Zhang (1994) to provide bounds for the prices of the expected payoffs for options, given the first two moments and skewness and kurtosis.

This paper first reviews alternative methods for determining option bounds. This method includes Stochastic dominance, linear programming, semi-parametric method, and non-parametric method for European option. Then option bounds for American and Asian options are discussed. Finally, we discuss empirical applications in equities and equity indices, index futures, foreign exchange rates, and real options.

This chapter first reviews alternative methods for determining option bounds. This method includes stochastic dominance, linear programming, semi-parametric method, and non-parametric method for European option. Then option bounds for American and Asian options are discussed. Finally, we discuss empirical applications in equities and equity indices, index futures, foreign exchange rates, and real options.

This paper offers an alternative view supporting the risk-based explanation of the momentum effect. Using stochastic dominance criteria, we find that the winners portfolio and the losers portfolio do not dominate each other. In general, the winners portfolio dominates at the right-hand side of the distribution of returns while the losers portfolio dominates at the left-hand side of the distribution. Our empirical results imply that the momentum profits provide neither an arbitrage opportunity nor a welfare improvement for rational investors ex ante. We interpret the evidence as follows: momentum profits are consistent with the notion of market rationality and market efficiency and are likely to be explained by omitted risk factors. Our findings also suggest that one possible reason why some investors prefer losers is because of less downside risk.

Omega ratios have been introduced in [1] as a performance measure to compare the performance of different investment opportunities. It does not have some of the drawbacks of the famous Sharpe ratio. In particular, it is consistent with first order stochastic dominance. Omega ratios also have an interesting relation to expectiles, which found increasing interest recently as risk measures. There is some confusion in the literature about consistency with respect to second order stochastic dominance. In this paper, we clarify this and extend it to a consistency result with respect to stochastic dominance of order 1 + γ recently introduced in [2] and generalizing the classical concepts of stochastic dominance of first and second order. Several examples illustrate the usefulness of this result. Finally, some consistency results for even more general stochastic dominance rules are shown, including the concept of ϵ-almost stochastic dominance introduced in [3].

Levy and Levy (Management Science 2002) present data that, according to their claims, violate prospect theory. They suggest that prospect theory's hypothesis of an S-shaped value function, concave for gains and convex for losses, is incorrect. However, all the data of Levy and Levy are perfectly consistent with the predictions of prospect theory, as can be verified by simply applying prospect theory formulas. The mistake of Levy and Levy is that they, incorrectly, thought that probability weighting could be ignored.

In a classroom choice experiment with mixed gambles and moderate probabilities, we find severe violations of cumulative prospect theory (CPT) and of Markowitz stochastic dominance. Our results shed new light on the exchange between Levy and Levy (2002) and Wakker (2003) in this journal.

This paper surveys the most recent advances in the context of decision making under uncertainty, with an emphasis on the modeling of risk-averse preferences using the apparatus of axiomatically defined risk functionals, such as coherent measures of risk and deviation measures, and their connection to utility theory, stochastic dominance, and other more established methods.