A stochastic programming approach to multicriteria portfolio optimization

We study a stochastic programming approach to multicriteria multi-period portfolio optimization problem. We use a Single Index Model to estimate the returns of stocks from a market-representative index and a random walk model to generate scenarios on the possible values of the index return. We consider expected return, Conditional Value at Risk and liquidity as our criteria. With stocks from Istanbul Stock Exchange, we make computational studies for the two and three-criteria cases. We demonstrate the tradeoffs between criteria and show that treating these criteria simultaneously yields meaningful efficient solutions. We provide insights based on our experiments.     

Merton problem in a discrete market with frictions

We study the classical optimal investment and consumption problem of Merton in a discrete time model with frictions. Market friction causes the investor to lose wealth due to trading. This loss is modeled through a nonlinear penalty function of the portfolio adjustment. The classical transaction cost and the liquidity models are included in this abstract formulation. The investor maximizes her utility derived from consumption and the final portfolio position. The utility is modeled as the expected value of the discounted sum of the utilities from each step. At the final time, the stock positions are liquidated and a utility is obtained from the resulting cash value. The controls are the investment and the consumption decisions at each time. The utility function is maximized over all controls that keep the after liquidation value of the portfolio non-negative. A dynamic programming principle is proved and the value function is characterized as its unique solution with appropriate initial data. Optimal investment and consumption strategies are constructed as well.     

Synthesis,Spectroscopic Studies and Crystal Structure of <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>′-bis((thiophene-2-carboxamido)propyl)piperazine

Abstract  A new multidentate ligand N,N′-bis((thiophene-2-carboxamide)propyl)piperazine has been synthesized from the reaction of thiophene-2-carbonylchloride and 1,4-bis(3-aminopropyl)piperazine. The title compound has been characterized by elemental analysis, FT-IR, ¹H-NMR and ¹³C-NMR spectroscopic techniques. The crystal structure of the title compound (C₂₀H₃₀N₄O₂S₂Cl₂) has also been determined by X-ray analysis. The title compound crystallize in the monoclinic space group P2₁/c with a = 9.768(1), b = 12.895(1), c = 10.083(1) ?, β = 115.12(1)°, V = 1149.9(2) ?³, D _x = 1.425 g cm⁻³ and Z = 2. The crystal structure was solved by direct methods and refined by full-matrix least squares to a find R = 0.039 [I > 2σ (I)] for 2,786 observed reflections. Graphical Abstract  The (N,N’–bis((thiophene-2- carboxamido)propyl)piperazine) molecule has been synthesized and its molecule structure has been investigated by using , FT-IR, 13C NMR and 1H-NMR spectroscopic and crystallographic techniques.

Transcendence of some power series for Liouville number arguments

In this paper, we prove that some power series with rational coefficients take either values of rational numbers or transcendental numbers for the arguments from the set of Liouville numbers under certain conditions in the field of complex numbers. We then apply this result to an algebraic number field. In addition, we establish the p-adic analogues of these results and show that these results have analogues in the field of p-adic numbers.     

Synthesis and Spectroscopic Studies of Phenanthroimidazole-Imine Derivatives and Evaluation of Their Antioxidant Activity

The phenanthroimidazole derivatives are used in the drug industry in large scale. In this study four new phenanthroimidazole-imine derivatives were synthesized and their spectroscopic studies as well as their antioxidant behaviors were examined. Structural analyses were made by FT-IR, ¹H-NMR, ¹³C-NMR, LC-MS spectroscopy techniques. UV–vis absorption and emission spectroscopy techniques have been used to determine the photophysical characteristics of four newly synthesized phenanthroimidazoles. The maximum absorption and emission wavelengths, molar extinction coefficients (ε), singlet energy levels (Es), Stokes’ shift values (Δλ) of phenanthroimidazole-imine derivatives are given. Additionally, the antioxidant behavior of all compounds were investigated which the ascorbic acid used as standard molecule in present study.     

The Detailed Comparison of Cell Death Detected by Annexin V-PI Counterstain Using Fluorescence Microscope,Flow Cytometry and Automated Cell Counter in Mammalian and Microalgae Cells

The evaluation of cell wellness is an important task for molecular biology research. This mainly comprises the assessment for morphology and viability of culturing cells. Annexin V-Propidium iodide counterstaining has been currently one of the common and easy methods to discriminate apoptotic and necrotic cell profiles. The method is operated by fluorescence-based detection of counterstain via laser beam-employed instruments including flow cytometer, fluorescence microscope and automated cell counter. The detection is primarily conducted based on the same principle; however the efficiency of instruments may vary. Here we evaluated the efficiency of those instruments for the clear-cut detection of cell death through various mammalian and microalgae cell lines. To the best of our knowledge, this is the first study revealing comparative analyses of apoptotic and necrotic cells in mammalian and microalgae cells using Annexin V-PI counterstain detected by flow cytometer, fluorescence microscope and automated cell counter. Fluorescence microscope and cell counter instruments were also tested and compared for the traditional trypan blue-based cell viability detection performance. For these, cell death was induced by UV-irradiation and/or bee venom for mammalian (pancreatic cancer, metastatic breast cancer and mouse fibroblasts) and microalgae cells (Chlorella vulgaris), respectfully. Findings postulated that automated cell counter and fluorescence microscopy revealed similar patterns for the detection by both counterstain and trypan blue in mammalian cells. Interestingly, flow cytometry did provide an accurate and significant detection for only one mammalian cell line when UV-treatment was followed by routine Annexin V-Propidium iodide counterstaining. Unlike, only flow cytometry revealed a significant change in the detection of death of microalgae cells by Annexin V-Propidium iodide method, but both Annexin and conventional trypan blue methods were not applicable for the automated cell counter and microscopic detections for microalgae cells. The related outputs propose that the obtaining reliable quantitation strongly depends on cell type and instruments used. These suggest the necessity of optimization and validation endeavors before any cell death detection initiative. The analytical outcomes present insights into detailed assessment of cell death detection of eukaryotic cells and provide a direction to researchers to consider.     

On the Hamilton-Jacobi-Bellman equations in Banach spaces

This paper is concerned with a certain class of distributed parameter control problems. The value function of these problems is shown to be the unique viscosity solution of the corresponding Hamiltonian-Jacobi-Bellman equation. The main assumption is the existence of an increasing sequence of compact invariant subsets of the state space. In particular, this assumption is satisfied by a class of controlled delay equations. This research was partly supported by the Institute for Mathematics and Its Applications with funds provided by the National Science Foundation and the Office of Naval Research. The author is indebted to Professor P. L. Lions for stimulating discussions and helpful suggestions.     

Optimal control of a one-dimensional storage process

We consider the discounted and ergodic optimal control problems related to a one-dimensional storage process. The existence and uniqueness of the corresponding Bellman equation and the regularity of the optimal value is established. Using the Bellman equation an optimal feedback control is constructed. Finally we show that under this optimal control the origin is reachable.This work was supported by the National Science Foundation under Grant No. MCS 8121940.