Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

Reservoir operations optimization via fuzzy criterion decision processes

In this paper, we propose the treatment of complex reservoir operation problems via our newly developed tool of fuzzy criterion decision processes. This novel approach has been shown to be a more flexible and useful analysis tool especially when it is desirable to incorporate an expert’s knowledge into the decision models. Additionally, it has been demonstrated that this form of decision models will usually result in an optimal solution, which guarantees the highest satisfactory degree. We provide a practical exemplification procedure for the models presented as well as an application example.     

On the multi-attribute stopping problem with general value functions

We examine a sequential selection problem in which a single option must be selected. Each option's value is a function of its attributes, whose precise values can be ascertained at a given cost. We prove the optimality of a threshold stopping rule for a general class of objective functions.     

Radiation induced synthesis and swelling characterization of thermo-responsive N-isopropylacrylamide-co-ionic hydrogels

Two-component thermo-responsive hydrogels poly(N-isopropylacrylamide)-co-vinylbenzyltrimethylammonium chloride (NIPA-co-VBT) and poly(N-isopropylacrylamide)-co-p-sodium styrene sulphonate (NIPA-co-SSS) were prepared by using high energy gamma radiation. The gels were characterized by Fourier transformed infrared spectroscopy (FTIR), scanning electron microscopy (SEM) and sol-gel analysis. The presence of ionic monomers in NIPA leads to lower gel content. Introduction of ionic components in the matrix enhanced swelling extent but caused slower volume transition. The swelling studies in alcohol indicated that swelling extent was function of polarity of the swelling medium and all gels followed the order water > methanol > ethanol > iso-propanol. In mixed co-solvents (water-alcohol), they exhibit complex reentrant behavior. The co-polymer gels containing VBT swelled faster and to higher extent than those containing SSS. The dynamic swelling studies indicated that diffusion of water in PNIPA gel shifts from Fickian for PNIPA to anomalous for NIPA-co-ionic gels also the mean swelling time (MST) decreases for gels containing ionic monomers.     

Planned positron experiments at FRM-II

The new research reactor FRM-II near Munich has a strong positron source, which delivers an intense, nearly monoenergetic positron beam. Our positron systems, the pulsed low energy positron source (PLEPS) and the scanning positron microscope (SPM) will be operated at this beam. Some aspects of matching these systems to the new positron source will be discussed.Considerable improvements are expected, e.g. more than 10⁵ s⁻¹ recorded events at PLEPS and sub-micrometre resolution at SPM. They will enable investigations in so far inaccessible problems like the evaluation of annihilation characteristics and trapping constants of individual defects or studies of fast dynamical processes. In applied materials science complex defect structures will be studied which demand a resolution into many differing lifetimes, e.g. fractured specimens, wear, corrosion, etc. Also large series of measurements at small systematic modifications are planned. There is also the opportunity to analyse in addition the chemical microstructure of the specimens by means of a hydrogen microprobe and other ion beam techniques available close to FRM-II at the Technical University of Munich.     

微通道板增益疲劳机理研究

微通道板的增益疲劳是微通道板的主要问题之一，本文分析了微通道板的表面结构模型，同通道板活性表面上碱金属的逸出和碳的增加是导致微通道板的增益疲劳的主要原因，另外，探讨碱金属逸出的机理和碳污染的来源，介绍延长微通道板工作寿命的有效方法。     

含R_2dtc配体Mo-Cu化合物的动态~(95)Mo NMR

本实验利用动态~(95)Mo NMR监测Mo-Cu系列化合物的形成过程,对反应CuCl+NaR_2dtc+MoO_nS,摩尔比3:3:1,溶剂为DMF;R=Et,n=0(Ⅰ);R=Me,n=0(Ⅱ);R=Et,n=2(Ⅲ)进行了研究,观察到具有不同簇骼的多种中间产物的存在及随反应进程相互转化等现象。     

Macroporous poly(methyl methacrylate) produced by phase separation during polymerisation in solution

Polymethyl methacrylate (PMMA) sponges were obtained by polymerization in a solution with monomer/ethanol ratios up to 20:80. The material obtained after the elimination of the solvent present a homogeneous distribution of dispersed pores up to a monomer/ethanol ratio lower than 40:60. For higher ethanol contents in the reacting mixture, the morphology of the sponge corresponds to a network of PMMA microparticles, leaving large empty spaces leading to highly porous structure. The monomer/ethanol ratio during polymerization has a large influence on the porosity, thermal, and mechanical properties of the material and, for large solvent contents, on the size of the polymer microparticles.     

Electrochiroptical systems based on biphenyl-2,2′-diyl-type dicationic dyes: strong chiroptical signals through the transmission of point chirality to axial chirality

Huge CD amplitude (A = +538) was attained by diastereomeric preference (50% de) for the title dication with two bis[4-(R)-sec-butoxyphenyl]methylium units in benzene at 23 °C. Intramolecular π-π stacking is the origin for effective transmission of point chirality to axial chirality to attain the chiroptical enhancement of 400-times. Thanks to the strong CD signaling, chiroptical changes upon electrolysis could be readily detected, thus realizing a new class of electrochiroptical response systems. Chiroptical properties could also be modified by solvent polarity.     

Dynamic Interfacial Tension Behavior of Water/Oil Systems Containing In situ-Formed Surfactants

Time-dependent interfacial tension (IFT) has been investigated for an interfacially reactive immiscible system composed of model-acidified oil and alkaline water. The acidified oil was composed of either lauric acid or linoleic acid dissolved in n-dodecane. Drop volume tensiometry was employed to measure the interfacial tension between the two phases. In the case of lauric acid, the IFT value was found to decrease sharply with increasing alkali concentration, even at low drop formation times. In the case of linoleic acid, the IFT decrease with the drop formation time was more gradual, especially at low alkali concentration. The rate of formation of the interfacial area was also found to be dependent on alkali concentration.