On a particular mapping in Rn
نویسنده
چکیده
In this working paper we study some properties of a particular mapping in Rn related to an optimization problem with one equality constraint. We motivate the definition of the relevant mapping starting from a portfolio selection problem, in which we minimize the risk of an investment (the variance of its return) with one equality constraint given by a fixed level of the return itself. The vector of the optimal portfolio is given by a particular mapping of the vector of returns and this mapping is taken into consideration. All the properties of this mapping may of course be considered in the more general context of an optimization problem with one equality contraint, but some of them may be reasonably extended in the further general case of more equality contraints. Although it has not been investigated in this work, some results may have a relevant meaning in explaining the relation between the vector of expected returns and the optimal portfolio.
منابع مشابه
Diagnosis of patients with Parkinson's disease using quantitative susceptibility mapping
Introduction: Parkinson'sdisease isassociated withirondeposition in the brain. The T2-weighted imaging, T2* mapping, R2 mapping and Quantitative Susceptibility Mapping (QSM) are three common methods to evaluating the iron deposition in brain. Among three methods the QSM is more sensitive than others. Few studies have been used QSM for evaluating the iron deposition in the basa...
متن کاملModeling of Partial Digest Problem as a Network flows problem
Restriction Site Mapping is one of the interesting tasks in Computational Biology. A DNA strand can be thought of as a string on the letters A, T, C, and G. When a particular restriction enzyme is added to a DNA solution, the DNA is cut at particular restriction sites. The goal of the restriction site mapping is to determine the location of every site for a given enzyme. In partial digest metho...
متن کاملBelievable Visual Feedback in Motor Learning Using Occlusion-based Clipping in Video Mapping
Gait rehabilitation systems provide patients with guidance and feedback that assist them to better perform the rehabilitation tasks. Real-time feedback can guide users to correct their movements. Research has shown that the quality of feedback is crucial to enhance motor learning in physical rehabilitation. Common feedback systems based on virtual reality present interactive feedback in a monit...
متن کاملPacking Polynomials on Multidimensional Integer Sectors
Denoting the real numbers and the nonnegative integers, respectively, by R and N, let S be a subset of Nn for n = 1, 2, . . ., and f be a mapping from Rn into R. We call f a packing function on S if the restriction f |S is a bijection onto N. For all positive integers r1, . . . , rn−1, we consider the integer sector I(r1, . . . , rn−1) = {(x1, . . . , xn) ∈ Nn | xi+1 6 rixi for i = 1, . . . , n...
متن کاملOn fixed points of fundamentally nonexpansive mappings in Banach spaces
We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...
متن کامل