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.     

Effect of reaction conditions on the molecular weight and polydispersity of linear poly(arylene ether phosphine oxide)s prepared from an AB monomer

A thorough study of the polymerization behavior of 4‐fluoro‐4′‐hydroxytriphenyl‐phosphine oxide, 2 , under nucleophilic aromatic substitution reactions has been carried out. The synthesis of 2 was achieved in excellent yields by the reaction of bis(4‐fluorophenyl)phenylphosphine oxide, 1 , with one equivalent of potassium hydroxide in DMSO/water. The structure and purity of 2 were confirmed via ¹H, ¹³C, and ³¹P NMR spectroscopy along with elemental analysis. Polymerization reactions of 2 in NMP or DMSO at 180 °C provided the corresponding linear poly(arylene ether phosphine oxide)s, PAEPOs, with number average molecular weights, M_n, ranging from 11,700 to 36,500 Da. All of the polymer samples were completely soluble in chloroform, tetrahydrofuran, DMSO, NMP, and DMAc. The polymerization reactions were accompanied by a competing intramolecular process that resulted in the formation of cyclic oligomeric species that were removed via a final precipitation from methanol. Analysis using ³¹P NMR spectroscopy and size exclusion chromatography (SEC) confirmed that the majority of the lower molecular weight cyclic species were removed via this process. The polymer samples formed tough films when chloroform solutions were slowly evaporated on a glass slide. The PAEPO samples prepared in this study exhibited excellent thermal stability with T_d (5%) values between 503 and 542 in air while the glass transition temperatures ranged from 223 to 237 °C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2099–2106, 2006     

Numerical simulation of critical dependences for symmetric two-layered Josephson junctions

Partial critical dependences of the form current-magnetic field in a two-layered symmetric Josephson junction are modeled. A numerical experiment shows that, for the zero interaction coefficient between the layers of the junction, jumps of the critical currents corresponding to different distributions of the magnetic fluxes in the layers may appear on the critical curves. This fact allows a mathematical interpretation of the results of some recent experimental results for two-layered junctions as a consequence of discontinuities of partial critical curves.     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

La（NCS）3.4.5H2O和B15C5在乙醇中的相平衡及热化学研究

采用半微量相平衡方法测定了三元体系Ｌａ（ＮＣＳ）３．４．５Ｈ２Ｏ－Ｂ１５Ｃ５－Ｃ２Ｈ５ＯＨ在２９８．１５Ｋ的溶解度，测定了各饱和溶液的折光率。     

Effect of pressure on the solubilities ofo-,m- andp-xylene in water

The solubilities of o-, m- and p-xylene in water were measured at 25.0°C up to 250, 385, and 50 MPa, respectively. The solubility increased with increasing pressure up to 120 MPa (50 MPa for p-xylene) and then decreased. The reaction volumes, V^o accompanying the dissolution at 0.1 MPa were estimated as –3.6±0.5, –3.4±0.5, and –4.1±0.5 cm³-mol^–1 for o-, m-, and p-xylene, respectively, from the pressure dependences of the solubilities. The limiting partial molar volumes, of p- and o-xylene in water under high pressure were estimated from V^o and the molar volume of the xylene. The partial molar volumes decreased with increasing pressure. The reaction volume for the formation of intra-molecular pairwise hydrophobic interaction between the methyl groups, as proposed by Ben-Naim, is discussed for the V^o of p- and o-xylene at 0.1 MPa.     

Partial molal heat capacities of aqueous tetraalkylammonium bromides as functions of temperature

Enthalpies of solution have been measured from 5 to 85°C for aqueous tetraethyl- and tetrapropylammonium bromides, and the integral heat method is employed to evaluate for these electrolytes over a wide temperature range. Data taken from the literature have been used to evaluate for aqueous Bu₄NBr over a similar temperature range. These data, along with similar data for Me₄NBr, previously reported, have been used to evaluate absolute ionic heat capacities. While the absolute values agree only qualitatively with two other methods of division, the temperature dependences of the three methods essentially agree up to 65°C. Heat capacities due to structural effects on the solvent, obtained by subtracting the inherent heat capacities of the ions, are extraordinarily positive for all four tetraalkylammonium ions and have negative temperature coefficients, indicating that all four ions, including the tetramethylammonium ion, are structure-making ions.     

Preparation of AgBiVMoO/-Al2O3 Catalysts for the Partial Oxidation of Propane

A novel mixed sol method was developed for the preparation of supported catalysts. Analyses by means of XRD and BET show that a 40%AgBiVMoO/γ-Al2O3 catalyst prepared by this method possessed high specific surface area and high dispersion of the active phase. As a result, high acrylic acid selectivity of 8.5% was obtained when the catalyst was used in the reaction of propane partial oxidation to acrylic acid in a fixed-bed reactor.     

Diffusion in organic solvents: Interdiffusion coefficient of 1,1,2,2-tetrabromoethane

Interdiffusion coefficient have been measured for 1,1,2,2-tetrabromoethane in 21 organic solvents in order to ascertain the influence of shape, size, viscosity, nature and degree of branching, of the solvent molecules on transport properties. None of the existing correlations for diffusion in binary liquid systems appear to fit all the experimental data. Steric effects due to the solvent molecules are shown to be very important in the interpretation of the diffusion process.