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

Colour Text Segmentation in Web Images Based on Human Perception

There is a significant need to extract and analyse the text in images on Web documents, for effective indexing, semantic analysis and even presentation by non-visual means (e.g., audio). This paper argues that the challenging segmentation stage for such images benefits from a human perspective of colour perception in preference to RGB colour space analysis. The proposed approach enables the segmentation of text in complex situations such as in the presence of varying colour and texture (characters and background). More precisely, characters are segmented as distinct regions with separate chromaticity and/or lightness by performing a layer decomposition of the image. The method described here is a result of the authors’ systematic approach to approximate the human colour perception characteristics for the identification of character regions. In this instance, the image is decomposed by performing histogram analysis of Hue and Lightness in the HLS colour space and merging using information on human discrimination of wavelength and luminance

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

Models of Passive and Reactive Tracer Motion: an Application of Ito Calculus

By means of Ito calculus it is possible to find, in a straight-forward way, the analytical solution to some equations related to the passive tracer transport problem in a velocity field that obeys the multidimensional Burgers equation and to a simple model of reactive tracer motion.Comment: revised version 7 pages, Latex, to appear as a letter to J. of Physics

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

Mutual Fund Theorem for continuous time markets with random coefficients

We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving Brownian motion, and they are supposed to be currently observable. It is shown that some weakened version of Mutual Fund Theorem holds for this market for general class of utilities; more precisely, it is shown that the supremum of expected utilities can be achieved on a sequence of strategies with a certain distribution of risky assets that does not depend on risk preferences described by different utilities.Comment: 17 page