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.     

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.     

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.     

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.     

快速响应的温敏性聚(N-异丙基丙烯酰胺)水凝胶 Ⅰ.以CaCO_3为成孔剂制备方法、表征及动力学研究

以不同粒径的CaCO3粒子为成孔剂 ,合成了快速响应的温敏性聚 (N 异丙基丙烯酰胺 ) (PNIPA)水凝胶 .利用扫描电镜观察到水凝胶具有特殊的孔状结构 ,得到水凝胶的孔径大小为几十微米左右 .动力学研究表明 ,该水凝胶在温敏膨胀或收缩时 ,具有快速的响应速率 ,在 10min内的失水率可达 90 % .比较了干凝胶和4 0℃下失水后的凝胶两种不同状态下水凝胶的膨胀曲线 ,发现两者的溶胀动力学曲线明显不同 ,前者的曲线有拐点 .同时发现与失水收缩速率相比 ,水凝胶具有较慢的吸水膨胀速率 .     

1H NMR Study of Hindered Internal Rotation of Tetramethylthiuram Disulfide in Binary Dimethyl Sulfoxide‐Chloroform Mixtures

Hindered internal rotation about the C‐N single bonds joining the thiuram disulfide was studied by ¹H NMR complete line‐shaped analysis in different dimethyl sulfoxide‐chloroform (DMSO‐CDCl₃) mixtures. From the temperature dependence of methyls proton spectra, activation parameters (E_a, ΔH^≠, ΔS^≠, and ΔG^≠) were obtained. The Arrhenius plots showed a distinct isokinetic temperature at about 35 °C at which the exchange rate is more or less independent of the solvent composition. The resulting ΔH^≠ against TΔS^≠ plot showed a firmly good linear correlation, indicating the existence of an enthalpy‐entropy composition in an exchange process.