Pricing Spread Options using Matched Asymptotic Expansions

This document deals with approximating spread options prices using Matched Asymptotic Expansions techniques on the correlation. More precisely, it deals with spreads options on assets that are highly correlated (ρ ∼ 1), which is most commonly observed in Oil Markets (Crude Oil vs. Gasoline for example). We will first start by applying this methodology to exchange options before generalizing our results to spread options. Then we are going to describe an alternative approach of pricing spread options by approximating the bivariate normal distribution. Finally, we will see how we can apply our methodology to the case where we have more than two assets

q-Ehrhart polynomials of Gorenstein polytopes, Bernoulli umbra and related Dirichlet series

This article considers some q-analogues of classical results concerning the Ehrhart polynomials of Gorenstein polytopes, namely properties of their q-Ehrhart polynomial with respect to a good linear form. Another theme is a specific linear form {\Psi} (involving Carlitz' q-analogues of Bernoulli numbers) on the space of polynomials, for which one shows interesting behaviour on these q-Ehrhart polynomials. A third point is devoted to some related zeta-like functions associated with polynomialsComment: 16 page

Probabilistic modelling and inference of human behaviour from mobile phone time series

With an estimated 4.1 billion subscribers around the world, the mobile phone offers a unique opportunity to sense and understand human behaviour from location, co-presence and communication data. While the benefit of modelling this unprecedented amount of data is widely recognised, a number of challenges impede the development of accurate behaviour models. In this thesis, we identify and address two modelling problems and show that their consideration improves the accuracy of behaviour inference. We first examine the modelling of long-range dependencies in human behaviour. Human behaviour models only take into account short-range dependencies in mobile phone time series. Using information theory, we quantify long-range dependencies in mobile phone time series for the first time, demonstrate that they exhibit periodic oscillations and introduce novel tools to analyse them. We further show that considering what the user did 24 hours earlier improves accuracy when predicting user behaviour five hours or longer in advance. The second problem that we address is the modelling of temporal variations in human behaviour. The time spent by a user on an activity varies from one day to the next. In order to recognise behaviour patterns despite temporal variations, we establish a methodological connection between human behaviour modelling and biological sequence alignment. This connection allows us to compare, cluster and model behaviour sequences and introduce novel features for behaviour recognition which improve its accuracy. The experiments presented in this thesis have been conducted on the largest publicly available mobile phone dataset labelled in an unsupervised fashion and are entirely repeatable. Furthermore, our techniques only require cellular data which can easily be recorded by today's mobile phones and could benefit a wide range of applications including life logging, health monitoring, customer profiling and large-scale surveillance