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Two topics in financial mathematics : Forward utility and consumption functions & Hedging with variance swaps in infinite dimensions
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-10)
Financial Mathematics is often presented as being composed of two main branches: one dealing with investment and consumption, with the aim of answering the now ancient question of how people should invest and spend their ...
Automorphisms of free products of groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2013-02-05)
The symmetric automorphism group of a free product is a group rich in algebraic structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology ...
Morita cohomology
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2014-01-07)
This work constructs and compares different kinds of categorified cohomology of a locally contractible topological space X. Fix a commutative ring k of characteristic 0 and also denote by k the differential graded category ...
A 3-manifold group which is not four dimensional linear
(ElsevierJournal of Pure and Applied Algebra, 2014-01-28)
We give examples of closed orientable graph 3-manifolds having a fundamental group which is not a subgroup of GL(4, F) for any field F. This answers a question in the Kirby problem list from 1977 which is credited to the ...
New approaches to modern statistical classification problems
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2015-11-10)
This thesis concerns the development and mathematical analysis of statistical procedures for
classification problems. In supervised classification, the practitioner is presented with the
task of assigning an object to ...
Discussion of ‘An adaptive resampling test for detecting the presence of significant predictors’ by I. W. McKeague and M. Qian
(Taylor & FrancisJournal of the American Statistical Association, 2016-01-15)
We are grateful for the opportunity to discuss this new test, based on marginal screening, of a global null hypothesis in linear models. Marginal screening has become a very popular tool for reducing dimensionality in ...
Stability and bifurcation for the Kuramoto model
(ElsevierJournal de Mathématiques Pures et Appliquées, 2015-11-11)
We study the mean-field limit of the Kuramoto model of globally coupled oscillators. By studying the evolution in Fourier space and understanding the domain of dependence, we show a global stability result. Moreover, we ...
A More General Pandora Rule?
(ElsevierJournal of Economic Theory, 2015-11-02)
In a model introduced by Weitzman an agent called Pandora opens boxes sequentially, in whatever order she likes, discovers prizes within, and optimally stops. Her aim is to maximize the expected value of the greatest ...
Optimal impartial selection
(Society for Industrial and Applied MathematicsSIAM Journal on Computing, 2015-10-20)
We study a fundamental problem in social choice theory, the selection of a member of a set of agents based on impartial nominations by agents from that set. Studied previously by Alon et al. [Proceedings of TARK, 2011, pp. ...
Critical behaviour in charging of electric vehicles
(IOP PublishingNew Journal of Physics, 2015-09-02)
The increasing penetration of electric vehicles over the coming decades, taken together with the high cost to upgrade local distribution networks and consumer demand for home charging, suggest that managing congestion on ...