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Mathematics and Statistics40%

Selected Abstracts

Quantum phenomena via complex measure: Holomorphic extension

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7 2006
Article first published online: 11 MAY 200, S.K. Srinivasan
The complex measure theoretic approach proposed earlier is reviewed and a general version of density matrix as well as conditional density matrix is introduced. The holomorphic extension of the complex measure density (CMD) is identified to be the Wigner distribution function of the conventional quantum mechanical theory. A variety of situations in quantum optical phenomena are discussed within such a holomorphic complex measure theoretic framework. A model of a quantum oscillator in interaction with a bath is analyzed and explicit solution for the CMD of the coordinate as well as the Wigner distribution function is obtained. A brief discussion on the assignment of probability to path history of the test oscillator is provided. [source]

A Direct Test for Cointegration Between a Pair of Time Series

JOURNAL OF TIME SERIES ANALYSIS, Issue 2 2002
STEPHEN J. LEYBOURNE
In this paper we introduce a new test of the null hypothesis of no cointegration between a pair of time series. For a very simple generating model, our test compares favourably with the Engle,Granger/Dickey,Fuller test and the Johansen trace test. Indeed, shortcomings of the former motivated the development of our test. The applicability of our test is extended to series generated by low-order vector autoregressions. Again, we find evidence that this general version of our test is more powerful than the Johansen test. The paper concludes with an empirical example in which the new test finds strong evidence of cointegration, but the Johansen test does not. [source]

A Fundamental Theorem of Asset Pricing for Large Financial Markets

MATHEMATICAL FINANCE, Issue 4 2000
Irene KleinArticle first published online: 25 DEC 200
We formulate the notion of "asymptotic free lunch" which is closely related to the condition "free lunch" of Kreps (1981) and allows us to state and prove a fairly general version of the fundamental theorem of asset pricing in the context of a large financial market as introduced by Kabanov and Kramkov (1994). In a large financial market one considers a sequence (Sn)n=1, of stochastic stock price processes based on a sequence (,n, Fn, (Ftn)t,In, Pn)n=1, of filtered probability spaces. Under the assumption that for all n, N there exists an equivalent sigma-martingale measure for Sn, we prove that there exists a bicontiguous sequence of equivalent sigma-martingale measures if and only if there is no asymptotic free lunch (Theorem 1.1). Moreover we present an example showing that it is not possible to improve Theorem 1.1 by replacing "no asymptotic free lunch" by some weaker condition such as "no asymptotic free lunch with bounded" or "vanishing risk." [source]

An economic application of the Dubovitskii,Milyutin version of the Maximum Principle

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2007
Siu Fai Leung
Abstract The Pontryagin Maximum Principle is well known in economics. There is a different and more general version of the Maximum Principle, first established by Dubovitskii and Milyutin (Dokl. Acad. Nauk SSSR 1963; 149:759,762; Zh. Vychisl. Mat. Mat. Fiz. 1965; 5:393,453), which is little known in economics and has never been applied to solve an economic optimal control problem. This paper introduces the Dubovitskii,Milyutin version of the Maximum Principle to economics and offers an economic application to illustrate the limitation of the conventional Maximum Principle and the usefulness of the Dubovitskii,Milyutin version. The Dubovitskii,Milyutin Maximum Principle should be an integral part of the economist's toolbox and be included in economics textbooks on dynamic optimization. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Variable Selection for Logistic Regression Using a Prediction-Focused Information Criterion

BIOMETRICS, Issue 4 2006
Gerda Claeskens
Summary In biostatistical practice, it is common to use information criteria as a guide for model selection. We propose new versions of the focused information criterion (FIC) for variable selection in logistic regression. The FIC gives, depending on the quantity to be estimated, possibly different sets of selected variables. The standard version of the FIC measures the mean squared error of the estimator of the quantity of interest in the selected model. In this article, we propose more general versions of the FIC, allowing other risk measures such as the one based on Lp error. When prediction of an event is important, as is often the case in medical applications, we construct an FIC using the error rate as a natural risk measure. The advantages of using an information criterion which depends on both the quantity of interest and the selected risk measure are illustrated by means of a simulation study and application to a study on diabetic retinopathy. [source]