We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration is provided.

Abstract. Mean-variance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of single-period variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development and theoretical analysis of multiperiod models based on scenario trees. A key property is the possibility of removing surplus money in future decisions, yielding approximate downside risk minimization.

Abstract. We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose mean–risk models which are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of second-order stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean–risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations. 1.

Empirical research on Lower Partial Moment (LPM) has ignored its portfolio algorithms and the major benefit of such analysis: that its utility function is as general as the utility function assumed by stochastic dominance analysis. Since efficient algorithms for stochastic dominance do not exist, an LPM algorithm may be a viable substitute. This paper is concerned with the composition of portfolios selected by an LPM algorithm, specifically the effect on the characteristics of LPM-selected portfolios whenever the LPM utility function is changed throughout its range. I.

This paper discusses two optimal allocation problems. We consider different hypotheses of portfolio selection with stable distributed returns for each of them. In particular, we study the optimal allocation between a riskless return and risky stable distributed returns. Furthermore, we examine and compare the optimal allocation obtained with the Gaussian and the stable non-Gaussian distributional assumption for the risky return. KEY WORDS: optimal allocation, stochastic dominance, risk aversion, measure of risk, a stable distribution, domain of attraction, sub-Gaussian stable distributed, fund separation, normal distribution, mean variance analysis, safety-first analysis. 2 1. INTRODUCTION This paper serves a twofold objective: to compare the normal with the stable non-Gaussian distributional assumption when the optimal portfolio is to be chosen and to propose stable models for the optimal portfolio selection according to the utility theory under uncertainty. It is well-known that asset returns are not normally distributed, but many of the concepts in theoretical and empirical finance developed over the past decades rest upon the assumption that asset returns follow a normal distribution. The fundamental work of Mandelbrot (1963a-b, 1967a-b) and Fama (1963,1965a-b) has sparked considerable interest in studying the empirical distribution of financial assets. The excess kurtosis found in Mandelbrot's and Fama's investigations led them to reject the normal assumption and to propose the stable Paretian distribution as a statistical model for asset returns. The Fama and Mandelbrot's conjecture was supported by numerous empirical investigations in the subsequent years, (see Mittnik, Rachev and Paolella (1997) and Rachev and Mittnik (2000)). The practical and theoretical app...

Preference relations in ranking multivalued alternatives using stochastic dominance: case of the Warsaw Stock

Abstract. The mean-Gini approach is used to analyze stochastic externalities generated by agricultural production. The model addresses the problem of groundwater pollution caused by excessive fertilizer application. Inherent in the mean-Gini approach to expected utility maximization is a two-fold value: the simplicity of the two-parameter mean-variance model and satisfaction of necessary and sufficient conditions for stochastic dominance. Price and quantity policy recommendations to control externalities are formulated based upon the relative assessment of uncertainty by the regulatory authority and the farmers. Using the Gini as a measure of risk allows for the quantification of control policy measures under differentiated risk aversion and multiple sources of pollution. The model shows that when producers underestimate uncertainty, quota policies restricting fertilizer are more efficient than tax policies in reducing groundwater contamination. Key words. Stochastic externalities, water pollution policies, stochastic dominance. 1.

Comparing investments opportunities in emerging and developed market is an important issue in international portfolio management. However, it is well-established that the stock market returns are non-normal and have time-varying moments. This creates a challenge in ranking alternative investment strategies especially in a dynamic setting. We propse a distribution-free test based on a spatial dominance approach introduced by Park (2007) which is more general than the stochastic dominance approach allowing us to compare the sum of utilities obtained from alternative investments accumulated over a certain holding period instead of at the fixed point between the intervals. Applying the proposed test, we find that investments in emerging market is indifferent from their developed market counterparts for all investment horizon ranging from 3 month to 5 year, only if the currency risk is explicitly taken into account of. This suggests an integration between the two markets according to definition byBekaert and Harvey (2003). We also find that the returns of emerging market denominated in the local currency dominate those in the US dollar over 1- and 5-year investment horizons, implying that there is still an insufficient interaction between equity prices and foreign exchange rates in emerging markets in the longer-term. As expected, currency risk is found to be mostly irrelevant for developed market investments. JEL Classification: C14, G15.

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Abstract: This paper examines investor preferences for oil spot and futures based on mean-variance (MV) and stochastic dominance (SD). The mean-variance criterion cannot distinct the preferences of spot and market whereas SD tests leads to the conclusion that spot dominates futures in the downside risk while futures dominate spot in the upside profit. It is also found that risk-averse investors prefer investing in the spot index, whereas risk seekers are attracted to the futures index to maximize their expected utilities. In addition, the SD results suggest that there is no arbitrage opportunity between these two markets. Market efficiency and market rationality are likely to hold in the oil spot and futures markets.