A comparative analysis of the value of information in a continuous time market model with partial information: the cases of log-utility and CRRA

We study the question what value an agent in a generalized Black-Scholes model with partial information attributes to the complementary information. To do this, we study the utility maximization problems from terminal wealth for the two cases partial information and full information. We assume that the drift term of the risky asset is a dynamic process of general linear type and that the two levels of observation correspond to whether this drift term is observable or not. Applying methods from stochastic filtering theory we derive an analytical tractable formula for the value of information in the case of logarithmic utility. For the case of constant relative risk aversion (CRRA) we derive a semianalytical formula, which uses as an input the numerical solution of a system of ODEs. For both cases we present a comparative analysis

Detection of Minimum-Ionizing Particles and Nuclear Counter Effect with Pure BGO and BSO Crystals with Photodiode Read-out

Long BGO (Bismuth Germanate) and BSO (Bismuth Silicate) crystals coupled with silicon photodiodes have been used to detect minimum-ionizing particles(MIP). With a low noise amplifier customized for this purpose, the crystals can detect MIPs with an excellent signal-to-noise ratio. The NCE(Nuclear Counter Effect} is also clearly observed and measured. Effect of full and partial wrapping of a reflector around the crystal on light collection is also studied.Comment: 18 pages, including 5 figures; LaTeX and EP

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess $\delta$. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ($\rho_c, \delta_c$) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of $\delta_c$ is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, $\delta_c$ does not depend sensitively on the choice of the parameter $\gamma$ in Skyrme interaction.Comment: 15 pages, 9 figure

Nuclear matter properties and relativistic mean-field theory

Nuclear matter properties are calculated in the relativistic mean field theory by using a number of different parameter sets. The result shows that the volume energy $a_1$ and the symmetry energy $J$ are around the acceptable values 16MeV and 30MeV respectively; the incompressibility $K_0$ is unacceptably high in the linear model, but assumes reasonable value if nonlinear terms are included; the density symmetry $L$ is around $100MeV$ for most parameter sets, and the symmetry incompressibility $K_s$ has positive sign which is opposite to expectations based on the nonrelativistic model. In almost all parameter sets there exists a critical point $(\rho_c, \delta_c)$, where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero, falling into ranges 0.014fm$^{-3}<\rho_c<0.039$fm$^{-3}$ and $0.74<\delta_c\le0.95$; for a few parameter sets there is no critical point and the pure neutron matter is predicted to be bound. The maximum mass $M_{NS}$ of neutron stars is predicted in the range 2.45M$_\odot\leq M_{NS}\leq 3.26$M$_\odot$, the corresponding neutron star radius $R_{NS}$ is in the range 12.2km$\leq R_{NS}\leq 15.1$km.Comment: 10 pages, 5 figure

Quantising Higher-spin String Theories

In this paper, we examine the conditions under which a higher-spin string theory can be quantised. The quantisability is crucially dependent on the way in which the matter currents are realised at the classical level. In particular, we construct classical realisations for the $W_{2,s}$ algebra, which is generated by a primary spin-$s$ current in addition to the energy-momentum tensor, and discuss the quantisation for $s\le8$. From these examples we see that quantum BRST operators can exist even when there is no quantum generalisation of the classical $W_{2,s}$ algebra. Moreover, we find that there can be several inequivalent ways of quantising a given classical theory, leading to different BRST operators with inequivalent cohomologies. We discuss their relation to certain minimal models. We also consider the hierarchical embeddings of string theories proposed recently by Berkovits and Vafa, and show how the already-known $W$ strings provide examples of this phenomenon. Attempts to find higher-spin fermionic generalisations lead us to examine the whether classical BRST operators for $W_{2,{n\over 2}}$ ($n$ odd) algebras can exist. We find that even though such fermionic algebras close up to null fields, one cannot build nilpotent BRST operators, at least of the standard form.Comment: CTP TAMU-24/94, KUL-TF-94/11, SISSA-135/94/E