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

Linear Toric Fibrations

These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations. Polarized toric varieties which are birationally equivalent to projective toric bundles are associated to a class of polytopes called Cayley polytopes. Their geometry and combinatorics have a fruitful interplay leading to fundamental insight in both directions. These notes will illustrate geometrical phenomena, in algebraic geometry and neighboring fields, which are characterized by a Cayley structure. Examples are projective duality of toric varieties and polyhedral adjunction theory

Subtle competition between ferromagnetic and antiferromagnetic order in a Mn(II) - free radical ferrimagnetic chain

The macroscopic magnetic characterization of the Mn(II) - nitronyl nitroxide free radical chain (Mn(hfac)2(R)-3MLNN) evidenced its transition from a 1-dimensional behavior of ferrimagnetic chains to a 3-dimensional ferromagnetic long range order below 3 K. Neutron diffraction experiments, performed on a single crystal around the transition temperature, led to a different conclusion : the magnetic Bragg reflections detected below 3 K correspond to a canted antiferromagnet where the magnetic moments are mainly oriented along the chain axis. Surprisingly in the context of other compounds in this family of magnets, the interchain coupling is antiferromagnetic. This state is shown to be very fragile since a ferromagnetic interchain arrangement is recovered in a weak magnetic field. This peculiar behavior might be explained by the competition between dipolar interaction, shown to be responsible for the antiferromagnetic long range order below 3 K, and exchange interaction, the balance between these interactions being driven by the strong intrachain spin correlations. More generally, this study underlines the need, in this kind of molecular compounds, to go beyond macroscopic magnetization measurements.Comment: 12 pages, 10 figures, submitted to Phys. Rev.

Quantum spin fluctuations in the dipolar Heisenberg-like rare earth pyrochlores

The magnetic pyrochlore oxide materials of general chemical formula R2Ti2O7 and R2Sn2O7 (R = rare earth) display a host of interesting physical behaviours depending on the flavour of rare earth ion. These properties depend on the value of the total magnetic moment, the crystal field interactions at each rare earth site and the complex interplay between magnetic exchange and long-range dipole-dipole interactions. This work focuses on the low temperature physics of the dipolar isotropic frustrated antiferromagnetic pyrochlore materials. Candidate magnetic ground states are numerically determined at zero temperature and the role of quantum spin fluctuations around these states are studied using a Holstein-Primakoff spin wave expansion to order 1/S. The results indicate the strong stability of the proposed classical ground states against quantum fluctuations. The inclusion of long range dipole interactions causes a restoration of symmetry and a suppression of the observed anisotropy gap leading to an increase in quantum fluctuations in the ground state when compared to a model with truncated dipole interactions. The system retains most of its classical character and there is little deviation from the fully ordered moment at zero temperature.Comment: Latex2e, 18 pages, 4 figures, IOP forma

Finite size errors in quantum many-body simulations of extended systems

Further developments are introduced in the theory of finite size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced Model Periodic Coulomb interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be applied consistently to all Coulomb interactions in the system. The Model Periodic Coulomb interaction greatly reduces the finite size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground and excited state calculations. We demonstrate that the finite size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar.Comment: 15 pages, 6 figures. To appear in Phys. Rev.

Social sciences research in neglected tropical diseases 2: A bibliographic analysis

The official published version of the article can be found at the link below.Background There are strong arguments for social science and interdisciplinary research in the neglected tropical diseases. These diseases represent a rich and dynamic interplay between vector, host, and pathogen which occurs within social, physical and biological contexts. The overwhelming sense, however, is that neglected tropical diseases research is a biomedical endeavour largely excluding the social sciences. The purpose of this review is to provide a baseline for discussing the quantum and nature of the science that is being conducted, and the extent to which the social sciences are a part of that. Methods A bibliographic analysis was conducted of neglected tropical diseases related research papers published over the past 10 years in biomedical and social sciences. The analysis had textual and bibliometric facets, and focussed on chikungunya, dengue, visceral leishmaniasis, and onchocerciasis. Results There is substantial variation in the number of publications associated with each disease. The proportion of the research that is social science based appears remarkably consistent (<4%). A textual analysis, however, reveals a degree of misclassification by the abstracting service where a surprising proportion of the "social sciences" research was pure clinical research. Much of the social sciences research also tends to be "hand maiden" research focused on the implementation of biomedical solutions. Conclusion There is little evidence that scientists pay any attention to the complex social, cultural, biological, and environmental dynamic involved in human pathogenesis. There is little investigator driven social science and a poor presence of interdisciplinary science. The research needs more sophisticated funders and priority setters who are not beguiled by uncritical biomedical promises

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Measurement of polarisation observables in Ks0Σ+K^0_s\Sigma^+ photoproduction off the proton

The reaction $\gamma \, p \rightarrow K^0_S\,\Sigma^+$ is studied in the photon energy range from threshold. Linearly polarised photon beams from coherent bremsstrahlung enabled the first measurement of photon beam asymmetries in this reaction up to $E_\gamma = 2250$ MeV. In addition, the recoil hyperon polarisation was determined through the asymmetry in the weak decay $\Sigma^+ \rightarrow p \pi^0$ up to $E_\gamma = 1650$ MeV. The data are compared to partial wave analyses, and the possible impact on the interpretation of a recently observed cusp-like structure near the $K^*$ thresholds is discussed.Comment: 6 pages, 5 figures. References [8,9,10,11] which were not on the original submission are now include

Localizing gravity on a 't Hooft-Polyakov monopole in seven dimensions

We present regular solutions for a brane world scenario in the form of a 't Hooft-Polyakov monopole living in the three-dimensional spherical symmetric transverse space of a seven-dimensional spacetime. In contrast to the cases of a domain-wall in five dimensions and a string in six dimensions, there exist gravity-localizing solutions for both signs of the bulk cosmological constant. A detailed discussion of the parameter space that leads to localization of gravity is given. A point-like monopole limit is discussed.Comment: 29 pages, 17 figure

Graphite and Hexagonal Boron-Nitride Possess the Same Interlayer Distance. Why?

Graphite and hexagonal boron nitride (h-BN) are two prominent members of the family of layered materials possessing a hexagonal lattice. While graphite has non-polar homo-nuclear C-C intra-layer bonds, h-BN presents highly polar B-N bonds resulting in different optimal stacking modes of the two materials in bulk form. Furthermore, the static polarizabilities of the constituent atoms considerably differ from each other suggesting large differences in the dispersive component of the interlayer bonding. Despite these major differences both materials present practically identical interlayer distances. To understand this finding, a comparative study of the nature of the interlayer bonding in both materials is presented. A full lattice sum of the interactions between the partially charged atomic centers in h-BN results in vanishingly small monopolar electrostatic contributions to the interlayer binding energy. Higher order electrostatic multipoles, exchange, and short-range correlation contributions are found to be very similar in both materials and to almost completely cancel out by the Pauli repulsions at physically relevant interlayer distances resulting in a marginal effective contribution to the interlayer binding. Further analysis of the dispersive energy term reveals that despite the large differences in the individual atomic polarizabilities the hetero-atomic B-N C6 coefficient is very similar to the homo-atomic C-C coefficient in the hexagonal bulk form resulting in very similar dispersive contribution to the interlayer binding. The overall binding energy curves of both materials are thus very similar predicting practically the same interlayer distance and very similar binding energies.Comment: 18 pages, 5 figures, 2 table