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The Efficient Frontier in Randomized Social Choice  [PDF]
Timo Mennle,Sven Seuken
Computer Science , 2015,
Abstract: Since the celebrated Gibbard-Satterthwaite impossibility results and Gibbard's 1977 extension for randomized rules, it is known that strategyproofness imposes severe restrictions on the design of social choice rules. In this paper, we employ approximate strategyproofness and the notion of score deficit to study the possible and necessary trade-offs between strategyproofness and efficiency in the randomized social choice domain. In particular, we analyze which social choice rules make optimal trade-offs, i.e., we analyze the efficient frontier. Our main result is that the efficient frontier consists of two building blocks: (1) we identify a finite set of "manipulability bounds" B and the rules that are optimal at each of them; (2) for all other bounds not in B, we show that the optimal rules at those bounds are mixtures of two rules that are optimal at the two nearest manipulability bounds from B. We provide algorithms that exploit this structure to identify the entire efficient frontier for any given scoring function. Finally, we provide applications of our results to illustrate the structure of the efficient frontier for the scoring functions v=(1,0,0) and v=(1,1,0).
Estimating the NIH Efficient Frontier  [PDF]
Dimitrios Bisias, Andrew W. Lo, James F. Watkins
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0034569
Abstract: Background The National Institutes of Health (NIH) is among the world’s largest investors in biomedical research, with a mandate to: “…lengthen life, and reduce the burdens of illness and disability.” Its funding decisions have been criticized as insufficiently focused on disease burden. We hypothesize that modern portfolio theory can create a closer link between basic research and outcome, and offer insight into basic-science related improvements in public health. We propose portfolio theory as a systematic framework for making biomedical funding allocation decisions–one that is directly tied to the risk/reward trade-off of burden-of-disease outcomes. Methods and Findings Using data from 1965 to 2007, we provide estimates of the NIH “efficient frontier”, the set of funding allocations across 7 groups of disease-oriented NIH institutes that yield the greatest expected return on investment for a given level of risk, where return on investment is measured by subsequent impact on U.S. years of life lost (YLL). The results suggest that NIH may be actively managing its research risk, given that the volatility of its current allocation is 17% less than that of an equal-allocation portfolio with similar expected returns. The estimated efficient frontier suggests that further improvements in expected return (89% to 119% vs. current) or reduction in risk (22% to 35% vs. current) are available holding risk or expected return, respectively, constant, and that 28% to 89% greater decrease in average years-of-life-lost per unit risk may be achievable. However, these results also reflect the imprecision of YLL as a measure of disease burden, the noisy statistical link between basic research and YLL, and other known limitations of portfolio theory itself. Conclusions Our analysis is intended to serve as a proof-of-concept and starting point for applying quantitative methods to allocating biomedical research funding that are objective, systematic, transparent, repeatable, and expressly designed to reduce the burden of disease. By approaching funding decisions in a more analytical fashion, it may be possible to improve their ultimate outcomes while reducing unintended consequences.
Study on the Efficient Frontier of the Public Service Management  [cached]
Jie Ma
Asian Social Science , 2010, DOI: 10.5539/ass.v6n4p129
Abstract: The essential of the efficient frontier of the public service management is to confirm the power selection of the government, the market and the society, and the implementation frontier. In the frame of three-dimensional power, the simple combination of these powers would not form the efficient frontier of the public service management. Therefore, based on the power property and function, these powers must be divided and adjusted with reasonable system arrangement. The generation of the efficient frontier of the public service management is not to share or deny which one power, but maintain a dynamic balance of these three powers. With the advancement and development of the society, though the efficient frontier of the public service management will move slightly, but the substitution effect among powers will not happen.
On the Computation of the Efficient Frontier of the Portfolio Selection Problem
Clara Calvo,Carlos Ivorra,Vicente Liern
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/105616
Abstract: An easy-to-use procedure is presented for improving the -constraint method for computing the efficient frontier of the portfolio selection problem endowed with additional cardinality and semicontinuous variable constraints. The proposed method provides not only a numerical plotting of the frontier but also an analytical description of it, including the explicit equations of the arcs of parabola it comprises and the change points between them. This information is useful for performing a sensitivity analysis as well as for providing additional criteria to the investor in order to select an efficient portfolio. Computational results are provided to test the efficiency of the algorithm and to illustrate its applications. The procedure has been implemented in Mathematica.
Portfolio Evaluation Based on Efficient Frontier Superiority Using Center of Gravity
Zulkifli Mohamed,Daud Mohamad,Omar Samat
Journal of Applied Computer Science & Mathematics , 2010,
Abstract: Investing in portfolio of assets is the best way to reduce the investment risk. The most desired portfolio can be obtained when investors chose to invest in the portfolios that lay on the portfolio’s efficient frontier. However, the superiorities of the portfolios are difficult to differentiate especially when the efficient frontier curves are overlapping. This paper proposed the portfolio’s efficient frontier center of gravity (CoG) and Euclidean distance to identify its superiority. A sample of 49 stocks of large-cap and small-cap were used to construct two hypothetical portfolios and its efficient frontiers. The Euclidean distance showed that the large-cap portfolio is superior and having wider feasible solutions compared to the small-cap portfolio. The results of new tool introduced are consistent with the conventional methods. Here the theoretical and practical implications are provided in light of the findings.
Determining an Efficient Frontier in a Stochastic Moment Setting
Christian Johannes Zimmer,Beat Matthias Niederhauser
Revista Brasileira de Finan?as , 2004,
Abstract: We analyze the problem of portfolio optimization under uncertainty in the assets return distribution. After characterizing the problem using a general formulation involving the product space of the return distribution with the parameter distribution, we propose the use of penalty functions to solve the resulting program. The connection to some important existing approaches is shown, and we then focus on two specific proposals with an important practical feature: the stability of the resulting portfolio composition under changing input variables. With high transaction costs and missing liquidity in some Brazilian markets, this stability feature is of great practical relevance. Finally, we show with an example from the Brazilian market that the penalty function approach does indeed increase stability, and seems to be a promising alternative whose long-range performance should be analyzed.
High Dimensionality Effects on the Efficient Frontier: A Tri-Nation Study  [PDF]
Rituparna Sen, Pulkit Gupta, Debanjana Dey
Journal of Data Analysis and Information Processing (JDAIP) , 2016, DOI: 10.4236/jdaip.2016.41002
Abstract: Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.
Analytic Solutions of Efficient Frontier and Efficient Portfolio with Singular Covariance Matrix

JIANG Chunfu,

系统科学与数学 , 2008,
Abstract: This paper is concerned with the portfolio selection model with singular covariance matrix by using the generalized inverse matrix. The sufficient and necessary condition for existing efficient portfolio is obtained, and also the analytic solutions of efficient portfolio and efficient frontier is derived, which generalize successfully the classic Markowitz model and are helpful to investigate portfolio efficient subset further.
Frontier estimation via kernel regression on high power-transformed data  [PDF]
Stéphane Girard,Pierre Jacob
Statistics , 2011,
Abstract: We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the bandwidth of the kernel goes to zero. We give conditions on these two parameters to obtain complete convergence and asymptotic normality. The good performance of the estimator is illustrated on some finite sample situations.
L1-optimal linear programming estimatorfor periodic frontier functions with Holder continuous derivative  [PDF]
Alexander Nazin,Stephane Girard
Statistics , 2014,
Abstract: We propose a new estimator based on a linear programming method for smooth frontiers of sample points. The derivative of the frontier function is supposed to be Holder continuous.The estimator is defined as a linear combination of kernel functions being sufficiently regular, covering all the points and whose associated support is of smallest surface. The coefficients of the linear combination are computed by solving a linear programming problem. The L1- error between the estimated and the true frontier functionsis shown to be almost surely converging to zero, and the rate of convergence is proved to be optimal.
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