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Optimization with stochastic dominance constraints
 SIAM Journal on Optimization
"... 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 the ..."
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Cited by 32 (5 self)
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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.
Markowitz revisited: meanvariance models in financial portfolio analysis
 SIAM Rev
, 2001
"... Abstract. Meanvariance 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 singleperiod variants, including semivariance models. Particular emphasis is laid on avo ..."
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Cited by 21 (1 self)
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Abstract. Meanvariance 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 singleperiod 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.
Frontiers of stochastically nondominated portfolios
 Econometrica
, 2003
"... 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 secondorder ..."
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Cited by 15 (3 self)
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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 secondorder 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.
The Problem Of Optimal Asset Allocation With Stable Distributed Returns
 Stochastic Processes and Functional Analysis, Dekker Series of Lecture Notes in Pure and Applied Mathematics
, 2004
"... 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 c ..."
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Cited by 7 (4 self)
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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 nonGaussian distributional assumption for the risky return. KEY WORDS: optimal allocation, stochastic dominance, risk aversion, measure of risk, a stable distribution, domain of attraction, subGaussian stable distributed, fund separation, normal distribution, mean variance analysis, safetyfirst analysis. 2 1. INTRODUCTION This paper serves a twofold objective: to compare the normal with the stable nonGaussian 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 wellknown 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 (1963ab, 1967ab) and Fama (1963,1965ab) 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...
The Characteristics of Portfolios Selected by nDegree Lower Partial Moment
 International Review of Financial Analysis
, 1992
"... 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 ..."
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Cited by 6 (2 self)
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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 LPMselected portfolios whenever the LPM utility function is changed throughout its range. I.
2003) : “Two Paradigms and Nobel Prizes in Economics: a Contradiction or Coexistence?”, NCCRFinrisk Working Paper No
"... Markowitz and Sharpe won the Nobel Prize in Economics for the development of MeanVariance (MV) analysis and the Capital Asset Pricing Model (CAPM). Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. In deriving the CAPM, Sharpe, Lintner and Mossin assume expected uti ..."
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Cited by 4 (3 self)
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Markowitz and Sharpe won the Nobel Prize in Economics for the development of MeanVariance (MV) analysis and the Capital Asset Pricing Model (CAPM). Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. In deriving the CAPM, Sharpe, Lintner and Mossin assume expected utility (EU) maximization in the face of risk aversion. Kahneman and Tversky suggest Prospect Theory (PT) as an alternative paradigm to EU theory. They show that investors distort probabilities, make decisions based on change of wealth, exhibit loss aversion and maximize the expectation of an Sshaped value function, which contains a riskseeking segment. Can these two apparently contradictory paradigms coexist? We show in this paper that although CPT (and PT) is in conflict to EUT, and violates some of the CAPM’s underlying assumptions, the Security Market Line Theorem (SMLT) of the CAPM is intact in the CPT framework. Therefore, the CAPM is intact also in CPT framework.
Capital Growth Theory and Practice
 Handbook of Asset and Liability Management, Vol. I: Theory and Methodology
, 2006
"... In capital accumulation under uncertainty, a decisionmaker must determine how much capital to invest in riskless and risky investment opportunities over time. The investment strategy yields a stream of capital, with investment decisions made so that the dynamic distribution of wealth has desirable ..."
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Cited by 3 (1 self)
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In capital accumulation under uncertainty, a decisionmaker must determine how much capital to invest in riskless and risky investment opportunities over time. The investment strategy yields a stream of capital, with investment decisions made so that the dynamic distribution of wealth has desirable properties. The distribution of accumulated capital to a fixed point in time and the distribution of the first passage time to a fixed level of accumulated capital are variables controlled by the investment decisions. An investment strategy which has many attractive and some not attractive properties is the growth optimal strategy, where the expected logarithm of wealth is maximized. This strategy is also referred to as the Kelly strategy It maximizes the rate of growth of accumulated capital.. With the Kelly strategy, the first passage time to arbitrary large wealth targets is minimized, and the probability of reaching those targets is maximized. However, the strategy is very aggressive since the ArrowPratt risk aversion index is essentially zero. Hence, the chances of losing a substantial portion of wealth are very high, particularly if the estimates of the returns distribution are in error. In the time domain, the chances are high
Multivariate concave and convex stochastic dominance
, 2010
"... Stochastic dominance permits a partial ordering of alternatives (probability distributions on consequences) based only on partial information about a decision maker’s utility function. Univariate stochastic dominance has been widely studied and applied, with general agreement on classes of utility f ..."
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Cited by 2 (0 self)
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Stochastic dominance permits a partial ordering of alternatives (probability distributions on consequences) based only on partial information about a decision maker’s utility function. Univariate stochastic dominance has been widely studied and applied, with general agreement on classes of utility functions for dominance of different degrees. Extensions to the multivariate case have received less attention and have used different classes of utility functions, some of which require strong assumptions about utility. We investigate multivariate stochastic dominance using a class of utility functions that is consistent with a basic preference assumption, can be related to wellknown characteristics of utility, and is a natural extension of the stochastic order typically used in the univariate case. These utility functions are multivariate risk averse, and reversing the preference assumption allows us to investigate stochastic dominance for utility functions that are multivariate risk seeking. We provide insight into these two contrasting forms of stochastic dominance, develop some criteria to compare probability distributions (hence alternatives) via multivariate stochastic dominance, and illustrate how this dominance could be used in practice to identify inferior alternatives.
A GameTheoretic Analysis of the ESP Game
, 2009
"... In recent years, there has been a great deal of progress in “Games with a Purpose,” interactive games that users play because they are fun, with the added benefit that they are doing useful work in the process. The ESP game, developed by von Ahn and Dabbish [7], is an example of such a game devised ..."
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Cited by 1 (0 self)
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In recent years, there has been a great deal of progress in “Games with a Purpose,” interactive games that users play because they are fun, with the added benefit that they are doing useful work in the process. The ESP game, developed by von Ahn and Dabbish [7], is an example of such a game devised to label images on the web. Since labeling images is a hard problem for computer vision algorithms and can be tedious and timeconsuming for humans, the ESP game provides humans with incentive to do useful work by being enjoyable to play. We present a simple gametheoretic model for the ESP game and characterize the equilibrium behavior of the model. We show that a simple change in the incentive structure can lead to different equilibrium structure. Our results suggest the possibility of formal incentive design in achieving desirable systemwide outcomes in this area of “human computation” in complementing existing considerations of robustness against cheating and human factors.
INCENTIVES AND STANDARDS IN AGENCY CONTRACTS
"... This paper studies the structure of statecontingent contracts in the presence of moral hazard and multitasking. Necessary and sufficient conditions for the presence of multitasking to lead to fixed payments instead of incentive schemes are identified. It is shown that the primary determinant of whe ..."
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Cited by 1 (1 self)
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This paper studies the structure of statecontingent contracts in the presence of moral hazard and multitasking. Necessary and sufficient conditions for the presence of multitasking to lead to fixed payments instead of incentive schemes are identified. It is shown that the primary determinant of whether multitasking leads to higher or lower powered incentives is the role that noncontractible outputs play in helping the agent deal with the production risk associated with the observable and contractible outputs. When the noncontractible outputs are risk substitutes and are socially undesirable, standards are never optimal. If the noncontractible outputs are socially desirable, standards are never optimal if the noncontractible outputs play a riskcomplementary role. 1.