1,721,034 research outputs found
Simple Varieties for Limited Precision Points
No full textGiven a finite set X of points and a tolerance epsilon representing the maximum error on the coordinates of each point, we address the problem of computing a simple polynomial f whose zero-locus Z(f) ``almost'' contains the points of X.
We propose a symbolic-numerical method that, starting from the knowledge of X and epsilon, determines a polynomial f whose degree is strictly bounded by the minimal degree of the lements of the vanishing ideal of X. Then we state the sufficient conditions for proving that Z(f) lies close to each point of X by less than epsilon. The validity of the proposed method relies on a combination of classical results of Computer Algebra and Numerical Analysis; its effectiveness is
illustrated with a number of examples
Risk-adjusted geometric diversified portfolios
No full textIn this paper, exploiting a geometric argument, a novel and intuitive approach to portfolio diversification is proposed. The risk-adjusted geometric diversified portfolio is obtained as the point that is equally distant, for a given distance, from the vertices of the simplex, as they represent the single asset portfolios, the worst portfolios in terms of diversification. The definition of risk-adjusted distance as a special case of weighted Euclidean distance permits to introduce the information on the risks of the assets composing the portfolio in a very general way. The closed form solution for the allocation problem is provided and interesting theoretical properties are proved. Further, a direct comparison with Rao’s Quad- ratic Entropy maximization problem is outlined, thus yielding a different perspective to the use of such entropy as a diversification measure. Finally, the effectiveness of our proposal is emphasized through a comprehensive empirical out-of-sample exercise on real financial data
A new crossing criterion to assess path-following performance for Unmanned Marine Vehicles
No full textThe reasons why maximum diversification is better than minimum risk, including in terms of risk
No full textIn well-defined experimental settings, we evaluate the out-of-sample performance of two asset allocation paradigms: minimum risk and maximum diversification. Specifically, for each given risk measure, we compare the optimal minimum risk allocation with the allocation obtained by maximizing a portfolio diversification measure induced by the same risk measure. The experiment is performed in an out-of-sample, long-only framework, accounting for proportional transaction costs and different lengths of both the estimation window and the holding period. The strategies are compared in terms of numerical stability, return, the Sharpe ratio, and risk, as measured through the same risk measures used for calculating the optimal allocation: variance of returns, mean absolute deviation, value at risk, and expected shortfall at significance levels of 1% and 5%. We show that the maximum diversification strategies are highly competitive, if not generally superior, to the risk minimization allocations. This result supports well-known empirical findings of naive investment strategies that are difficult to beat in practice. Risk minimization strategies require highly accurate forecasts of future returns to perform well. Moreover, these strategies exhibit extreme numerical instability, where even infinitesimal variations in the inputs can dramatically alter the optimal allocation. Therefore, implementation costs are high, significantly impairing performance. In contrast, maximum diversification strategies are less sensitive to minor changes in the input parameters, providing stable allocations that are less affected by transaction costs. Furthermore, these strategies do not require accurate predictions of future returns and are effective in controlling investment risk
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