A Convex Stochastic Optimization Problem Arising from Portfolio Selection

A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In literature the latter is solved by assuming {\it a priori} that the problem is well-posed (i.e., the supremum value is finite) and a Lagrange multiplier exists (and as a consequence the optimal solution is attainable). In this paper it is first shown, via various counter-examples, neither of these two assumptions needs to hold, and an optimal solution does not necessarily exist. These anomalies in turn have important interpretations in and impacts on the portfolio selection modeling and solutions. Relations among the non-existence of the Lagrange multiplier, the ill-posedness of the problem, and the non-attainability of an optimal solution are then investigated. Finally, explicit and easily verifiable conditions are derived which lead to finding the unique optimal solution.Comment: 15 page

An Anthropocentric Approach to Text Extraction from WWW Images

There is a significant need to analyse the text in images on WWW pages, both for effective indexing and for presentation by non-visual means (e.g., audio). This paper argues that the extraction of text from such images benefits from an anthropocentric approach in the distinction between colour regions. The novelty of the idea is the use of a human perspective of colour perception in preference to RGB colour space analysis. This enables the extraction of text in complex situations such as in the presence of varying colour and texture (characters and background). More precisely, characters are extracted as distinct regions with separate chromaticity and/or luminance by performing a layer decomposition of the image. The method described here is the first in our 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 Luminance and merging in the HLS colour space

Visual Representation of Text in Web Documents and Its Interpretation

This paper examines the uses of text and its representation on Web documents in terms of the challenges in its interpretation. Particular attention is paid to the significant problem of non-uniform representation of text. This non-uniformity is mainly due to the presence of semantically important text in image form as opposed to the standard encoded text. The issues surrounding text representation in Web documents are discussed in the context of colour perception and spatial representation. The characteristics of the representation of text in image form are examined and research towards interpreting these images of text is briefly described

Optimal arbitrage under model uncertainty

In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative investment rules over a given time horizon, and under any admissible configuration of model parameters that might materialize. One characterization is in terms of the smallest positive supersolution to a fully nonlinear parabolic partial differential equation of the Hamilton--Jacobi--Bellman type. Under appropriate conditions, this smallest supersolution is the value function of an associated stochastic control problem, namely, the maximal probability with which an auxiliary multidimensional diffusion process, controlled in a manner which affects both its drift and covariance structures, stays in the interior of the positive orthant through the end of the time-horizon. This value function is also characterized in terms of a stochastic game, and can be used to generate an investment rule that realizes such best possible outperformance of the market.Comment: Published in at http://dx.doi.org/10.1214/10-AAP755 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Semantics-Based Content Extraction in Typewritten Historical Documents

This paper presents a flexible approach to extracting content from scanned historical documents using semantic information. The final electronic document is the result of a "digital historical document lifecycle" process, where the expert knowledge of the historian/archivist user is incorporated at different stages. Results show that such a conversion strategy aided by (expert) user-specified semantic information and which enables the processing of individual parts of the document in a specialised way, produces superior (in a variety of significant ways) results than document analysis and understanding techniques devised for contemporary documents

Testing composite hypotheses via convex duality

We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft and Witting (Z. Wahrsch. Verw. Gebiete 7 (1967) 289--302), where sufficient optimality conditions are derived via Lagrange duality, we obtain necessary and sufficient optimality conditions via Fenchel duality under compactness assumptions. This approach also differs from the methodology developed in Cvitani\'{c} and Karatzas (Bernoulli 7 (2001) 79--97).Comment: Published in at http://dx.doi.org/10.3150/10-BEJ249 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Trading Strategies Generated Pathwise by Functions of Market Weights

Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently developed another methodology for the functional construction of portfolios, which leads to very simple conditions for strong relative arbitrage with respect to the market. In this paper, both of these notions of functional portfolio generation are generalized in a pathwise, probability-free setting; portfolio generating functions are substituted by path-dependent functionals, which involve the current market weights, as well as additional bounded-variation functions of past and present market weights. This generalization leads to a wider class of functionally-generated portfolios than was heretofore possible, and yields improved conditions for outperforming the market portfolio over suitable time-horizons.Comment: 45 pages, 3 figure

Object Proposals for Text Extraction in the Wild

Object Proposals is a recent computer vision technique receiving increasing interest from the research community. Its main objective is to generate a relatively small set of bounding box proposals that are most likely to contain objects of interest. The use of Object Proposals techniques in the scene text understanding field is innovative. Motivated by the success of powerful while expensive techniques to recognize words in a holistic way, Object Proposals techniques emerge as an alternative to the traditional text detectors. In this paper we study to what extent the existing generic Object Proposals methods may be useful for scene text understanding. Also, we propose a new Object Proposals algorithm that is specifically designed for text and compare it with other generic methods in the state of the art. Experiments show that our proposal is superior in its ability of producing good quality word proposals in an efficient way. The source code of our method is made publicly available.Comment: 13th International Conference on Document Analysis and Recognition (ICDAR 2015

Convex Duality in Constrained Portfolio Optimization

We study the stochastic control problem of maximizing expected utility from terminal wealth and/or consumption, when the portfolio is constrained to take values in a given closed, convex subset of R^d. The setting is that of a continuous-time, Itô process model for the underlying asset prices. General existence results are established for optimal portfolio/consumption strategies, by suitably embedding the constrained problem in an appropriate family of unconstrained ones, and finding a member of this family for which the corresponding optimal policy obeys the constraints. Equivalent conditions for optimality are obtained, and explicit solutions leading to feedback formulae are derived for special utility functions and for deterministic coefficients. Results on incomplete markets, on short-selling constraints and on different interest rates for borrowing and lending are covered as special cases. The mathematical tools are those of continuous-time martingales, convex analysis and duality theory

A fine-grained approach to scene text script identification

This paper focuses on the problem of script identification in unconstrained scenarios. Script identification is an important prerequisite to recognition, and an indispensable condition for automatic text understanding systems designed for multi-language environments. Although widely studied for document images and handwritten documents, it remains an almost unexplored territory for scene text images. We detail a novel method for script identification in natural images that combines convolutional features and the Naive-Bayes Nearest Neighbor classifier. The proposed framework efficiently exploits the discriminative power of small stroke-parts, in a fine-grained classification framework. In addition, we propose a new public benchmark dataset for the evaluation of joint text detection and script identification in natural scenes. Experiments done in this new dataset demonstrate that the proposed method yields state of the art results, while it generalizes well to different datasets and variable number of scripts. The evidence provided shows that multi-lingual scene text recognition in the wild is a viable proposition. Source code of the proposed method is made available online