Abstract—Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and c...

The cardinality constrained optimization problem (CCOP) is an where the maximum number of nonzero components any feasible point bounded. In this paper, by rewriting constraint as a requiring that must lie in union certain subspaces, we consider CCOP mathematical program with disjunctive subspaces constraints (MPDSC). Since subspace special case convex polyhedral set, MPDSC (MPDC). Using structu...

Given constants s1, s2, . . . , sG, we consider variables X = ∑ sg1[g ∈ A] and Y = ∑ sg1[g ∈ B] as random variables with a joint distribution determined by taking (A,B) as uniformly random among set pairs in which A has fixed cardinality m, B has fixed cardinality n, and the intersection A ∩ B has fixed size q. Arguments about without-replacement sampling give the marginal mean and variance of ...

It is well known that for each n ≡ 1 or 3 (mod 6) there is a planar Steiner quasigroup (briefly, squag) of cardinality n (Doyen (1969) and Quackenbush (1976)). A simple squag is semi-planar if every triangle either generates the whole squag or the 9-element subsquag (Quackenbush (1976)). In fact, Quakenbush has stated that there should be such semi-planar squags. In this paper, we construct a s...

In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The generalized model is formulated as a mixed integer quadratic programming (MIP) problem. The purpose of this paper is to investigate a continuous approach base...

A Cramér-Rao bound (CRB) for semi-blind channel estimators in redundant block transmission systems is derived. The derived CRB is valid for any system adopting a full-rank linear redundant precoder, including the popular cyclicprefixed orthogonal frequency-division multiplexing system. Simple forms of CRBs for multiple complex parameters, either unconstrained or constrained by a holomorphic fun...