Optimal consumption and investment with bounded downside risk for power utility functions

We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We compare the optimal solutions in form of optimal value, optimal control and optimal wealth to analogous problems under additional uniform risk bounds. Our proofs are partly based on solutions to Hamilton-Jacobi-Bellman equations, and we prove a corresponding verification theorem. This work was supported by the European Science Foundation through the AMaMeF programme.Comment: 36 page

First-passage theory of exciton population loss in single-walled carbon nanotubes reveals micron-scale intrinsic diffusion lengths

One-dimensional crystals have long range translational invariance which manifests as long exciton diffusion lengths, but such intrinsic properties are often obscured by environmental perturbations. We use a first-passage approach to model single-walled carbon nanotube (SWCNT) exciton dynamics (including exciton-exciton annihilation and end effects) and compare it to results from both continuous-wave and multi-pulse ultrafast excitation experiments to extract intrinsic SWCNT properties. Excitons in suspended SWCNTs experience macroscopic diffusion lengths, on the order of the SWCNT length, (1.3-4.7 um) in sharp contrast to encapsulated samples. For these pristine samples, our model reveals intrinsic lifetimes (350-750 ps), diffusion constants (130-350 cm^2/s), and absorption cross-sections (2.1-3.6 X 10^-17 cm^2/atom) among the highest previously reported.and diffusion lengths for SWCNTs.Comment: 6 pages, 3 figure

Motion in a Random Force Field

We consider the motion of a particle in a random isotropic force field. Assuming that the force field arises from a Poisson field in $\mathbb{R}^d$, $d \geq 4$, and the initial velocity of the particle is sufficiently large, we describe the asymptotic behavior of the particle

Comparison of a black-box model to a traditional numerical model for hydraulic head prediction

Two different methodologies for hydraulic head simulation were compared in this study. The first methodology is a classic numerical groundwater flow simulation model, Princeton Transport Code (PTC), while the second one is a black-box approach that uses Artificial Neural Networks (ANNs). Both methodologies were implemented in the Bavaria region in Germany at thirty observation wells. When using PTC, meteorological and geological data are used in order to compute the simulated hydraulic head following the calibration of the appropriate model parameters. The ANNs use meteorological and hydrological data as input parameters. Different input parameters and ANN architectures were tested and the ANN with the best performance was compared with the PTC model simulation results. One ANN was trained for every observation well and the hydraulic head change was simulated on a daily time step. The performance of the two models was then compared based on the real field data from the study area. The cases in which one model outperforms the other were summarized, while the use of one instead of the other depends on the application and further use of the model

Influence of Noise on Force Measurements

We demonstrate how the ineluctable presence of thermal noise alters the measurement of forces acting on microscopic and nanoscopic objects. We quantify this effect exemplarily for a Brownian particle near a wall subjected to gravitational and electrostatic forces. Our results demonstrate that the force measurement process is prone to artifacts if the noise is not correctly taken into account.Comment: 4 Pages, 4 Figures, Accepte

Product structure of heat phase space and branching Brownian motion

A generical formalism for the discussion of Brownian processes with non-constant particle number is developed, based on the observation that the phase space of heat possesses a product structure that can be encoded in a commutative unit ring. A single Brownian particle is discussed in a Hilbert module theory, with the underlying ring structure seen to be intimately linked to the non-differentiability of Brownian paths. Multi-particle systems with interactions are explicitly constructed using a Fock space approach. The resulting ring-valued quantum field theory is applied to binary branching Brownian motion, whose Dyson-Schwinger equations can be exactly solved. The presented formalism permits the application of the full machinery of quantum field theory to Brownian processes.Comment: 32 pages, journal version. Annals of Physics, N.Y. (to appear

A stochastic perturbation of inviscid flows

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a \holderspace{k}{\alpha} local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as $\nu \to 0$, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$.Comment: 13 pages, no figures

Bioactive natural products: facts, applications, and challenges

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Today, there are a strong debate and interest regarding the safety aspects of chemical preservatives addedwidely inmany food products to prevent mainly growth of spoilage and pathogenic microbes. Synthetic compounds are considered responsible for carcinogenic and teratogenic attributes and residual toxicity. To avoid the aforementioned problems, consumers and authorities have increased pressure on food manufacturers to substitute the harmful artificial additives with alternative, more effective, nontoxic, and natural sub-stances. In this context, the use of natural compounds with antimicrobial action presents an intriguing case. Natural antioxidants also demonstrate a wide range of biological and pharmacological activities and are considered to have bene