Portfolio Decisions with Higher Order Moments

In this paper, we address the global optimization of two interesting nonconvex problems in finance. We relax the normality assumption underlying the classical Markowitz mean-variance portfolio optimization model and consider the incorporation of skewness (third moment) and kurtosis (fourth moment). The investor seeks to maximize the expected return and the skewness of the portfolio and minimize its variance and kurtosis, subject to budget and no short selling constraints. In the first model, it is assumed that asset statistics are exact. The second model allows for uncertainty in asset statistics. We consider rival discrete estimates for the mean, variance, skewness and kurtosis of asset returns. A robust optimization framework is adopted to compute the best investment portfolio maximizing return, skewness and minimizing variance, kurtosis, in view of the worst-case asset statistics. In both models, the resulting optimization problems are nonconvex. We introduce a computational procedure for their global optimization.Mean-variance portfolio selection, Robust portfolio selection, Skewness, Kurtosis, Decomposition methods, Polynomial optimization problems

Decomposition-Based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems

We consider polynomial optimization problems pervaded by a sparsity pattern. It has been shown in [1, 2] that the optimal solution of a polynomial programming problem with structured sparsity can be computed by solving a series of semidefinite relaxations that possess the same kind of sparsity. We aim at solving the former relaxations with a decompositionbased method, which partitions the relaxations according to their sparsity pattern. The decomposition-based method that we propose is an extension to semidefinite programming of the Benders decomposition for linear programs [3] .Polynomial optimization, Semidefinite programming, Sparse SDP relaxations, Benders decomposition

Partitioning Procedure for Polynomial Optimization: Application to Portfolio Decisions with Higher Order Moments

We consider the problem of finding the minimum of a real-valued multivariate polynomial function constrained in a compact set defined by polynomial inequalities and equalities. This problem, called polynomial optimization problem (POP), is generally nonconvex and has been of growing interest to many researchers in recent years. Our goal is to tackle POPs using decomposition. Towards this goal we introduce a partitioning procedure. The problem manipulations are in line with the pattern used in the Benders decomposition [1], namely relaxation preceded by projection. Stengle’s and Putinar’s Positivstellensatz are employed to derive the so-called feasibility and optimality constraints, respectively. We test the performance of the proposed method on a collection of benchmark problems and we present the numerical results. As an application, we consider the problem of selecting an investment portfolio optimizing the mean, variance, skewness and kurtosis of the portfolio.Polynomial optimization, Semidefinite relaxations, Positivstellensatz, Sum of squares, Benders decomposition, Portfolio optimization

Crisis and sustainable business in Central and Eastern Europe: Haniel-Seminar discussion paper

--Internationalization,economic crisis,Russia,Hungary,Belarus

Can we build synthetic, multicellular systems by controlling developmental signaling in space and time?

Using biological machinery to make new, functional molecules is an exciting area in chemical biology. Complex molecules containing both ‘natural’ and ‘unnatural’ components are made by processes ranging from enzymatic catalysis to the combination of molecular biology with chemical tools. Here, we discuss applying this approach to the next level of biological complexity — building synthetic, functional biotic systems by manipulating biological machinery responsible for development of multicellular organisms. We describe recent advances enabling this approach, including first, recent developmental biology progress unraveling the pathways and molecules involved in development and pattern formation; second, emergence of microfluidic tools for delivering stimuli to a developing organism with exceptional control in space and time; third, the development of molecular and synthetic biology toolsets for redesigning or de novo engineering of signaling networks; and fourth, biological systems that are especially amendable to this approach

Entropy-driven enhanced self-diffusion in confined reentrant supernematics

We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter $S\simeq1$. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in confinement. Recent developments in the pulsed field gradient NMR technique are shown to provide favorable conditions for an experimental confirmation of our simulations.Comment: 10 pages, 5 figure

Characterization of the local temperature in space and time around a developing Drosophila embryo in a microfluidic device

This paper characterizes a microfluidic platform that differentially controls the temperature of each half of a living Drosophila melanogaster fruitfly embryo in space and time (E. M. Lucchetta, J. H. Lee, L. A. Fu, N. H. Patel and R. F. Ismagilov, Nature, 2005, 434, 1134-1138). This platform relies on laminar flow of two streams of liquid with different temperature, and on rapid prototyping in polydimethylsiloxane (PDMS). Here, we characterized fluid flow and heat transport in this platform both experimentally and by numerical simulation, and estimated the temperature distribution around and within the embryo by numerical simulation, to identify the conditions for creating a sharper temperature difference (temperature step) over the embryo. Embryos were removed from the device and immunostained histochemically for detection of Paired protein. Biochemical processes are sensitive to small differences in environmental temperature. The microfluidic platform characterized here could prove useful in understanding dynamics of biochemical networks as they respond to changes in temperature

Microfabrication inside capillaries using multiphase laminar flow patterning

The reaction of species in solutions flowing laminarly (without turbulent mixing) inside capillaries was used as the basis for a broadly applicable method of microfabrication. In this method, patterning occurs as a result of transport of reactive species to interfaces within the capillary by laminar flow. A wide range of chemistries can be used to generate structures with feature sizes of less than 5 micrometers and with spatial localization to within 5 micrometers. The method is applicable to the patterning of metals, organic polymers, inorganic crystals, and ceramics on the inner walls of preformed capillaries, using both additive and subtractive processes