Extend the ideas of Kan and Zhou paper on Optimal Portfolio Construction under parameter uncertainty

In this dissertation, we extend the ideas of Raymond Kan and Guofu Zhou for optimal portfolio construction under parameter uncertainty. Kan and Zhou proved analytically that under parameter uncertainty, investing in the sample tangency portfolio and the riskless is not optimal. Based on this idea we will approach the portfolio construction under parameter uncertainty in a different way. We will optimise the expected out-of-sample performance of a portfolio using a numerical approach. Using Monte Carlo simulations we will develop an algorithm that calculates the expected out-of-sample performance of any portfolio rule. We will then extend this algorithm in order to be able to input new portfolio rules and test their performance.\ud \ud The new portfolio rules we introduce are based on shrinkages for the mean and covariance matrix of the assets returns. These shrinkages will have some parameters that will be chosen so that we optimise the expected out-of-sample performance of the input portfolio rule. A comparison is then done between the portfolio rules we introduce and Kan and Zhou portfolio rules

Stable bundles as Frobenius morphism direct image

Let X be a smooth projective curve of genus $g\geq 2$ defined over an algebraically closed field k of characteristic $p>0$ and let $F:X\rightarrow X_{1}$ be the relative k-linear Frobenius map. We prove (Theorem 1.1) E is a stable bundle on $X_{1}$ with $I(E)= (p-1)(2g-2)$ if and only if E is the direct image of some stable bundle W on $X$.Comment: 4 page

Comment on "Multiple Bosonic Mode Coupling in Electron Self-Energy of (La2−x_{2-x}Srx_x)CuO4_4"

We calculate the photoemission spectral response using the extracted $\alpha^2F$ of Zhou et al (cond-mat/0405130) as an input and we find that the reported Re$\Sigma$ has more strucure than physically possible. Therefore, the "fine structure" most likely reflects the experimental noise.Comment: Comment on cond-mat/0405130, "energy resolution" improve

A note on the least number of edges of 3-uniform hypergraphs with upper chromatic number 2

AbstractThe upper chromatic number χ¯(H) of a hypergraph H=(X,E) is the maximum number k for which there exists a partition of X into non-empty subsets X=X1∪X2∪⋯∪Xk such that for each edge at least two vertices lie in one of the partite sets. We prove that for every n⩾3 there exists a 3-uniform hypergraph with n vertices, upper chromatic number 2 and ⌈n(n-2)/3⌉ edges which implies that a corresponding bound proved in [K. Diao, P. Zhao, H. Zhou, About the upper chromatic number of a co-hypergraph, Discrete Math. 220 (2000) 67–73] is best-possible