Rough volatility and portfolio optimisation under small transaction costs

The first chapter of the thesis presents the study of the linear-quadratic ergodic control problem of fractional Brownian motion. Ergodic control problems arise naturally in the context of small cost asymptotic expansion of utility maximisation problems with frictions. The optimal solution to the ergodic control problem is derived through the use of an infinite dimensional Markovian representation of fractional Brownian motion as a superposition of Ornstein-Uhlenbeck processes. This solution then allows to compute explicit formulas for the minimised objective value through the variance of the stationary distribution of the Ornstein-Uhlenbeck processes. Building on the first chapter, the second chapter of the thesis presents the main result. This is motivated by the problem an agent faces when trying to minimise her utility loss in the presence of quadratic trading costs in a rough volatility model. Minimising the utility loss amounts to studying a tracking problem of a target that depends on the rough volatility process. This tracking problem is minimised at leading order by an asymptotically optimal strategy that is closely linked to the ergodic control problem of fractional Brownian motion. This asymptotically optimal strategy is explicitly derived. Moreover, the leading order of the small cost expansion is shown to depend only on the roughest part of the considered target. It therefore depends on the Hurst parameter. The third chapter is devoted to a numerical analysis of the utility loss studied in the second chapter. For this, we compare the utility loss in a rough volatility model to a semimartingale stochastic volatility model. The parameter values for both models are fitted to match frictionless utility for realistic values. By applying the result obtained in the second chapter of the thesis, the difference between leading order of utility loss can be explicitly compared

Pitfalls in measuring the endocannabinoid 2-arachidonoyl glycerol in biological samples

Background: The endocannabinoid 2-arachidonoyl glycerol (2-AG) undergoes spontaneous isomerization to biologically inactive 1-AG. This effect has not been adequately addressed in previous studies that reported 2-AG concentrations in biological samples. Methods: Liquid chromatography tandem-mass spectrometry (LC-MS/MS) was used for 1-AG and 2-AG analyses. Results: Identical collision-induced disintegration spectra were found for 1-AG and 2-AG. For specific detection of both compounds, which share a common mass transition, baseline chromatographic separation is mandatory, even when applying MS/MS technology with its generally high detection specificity. When using standard chromatographic conditions with the very short run times typically used in LC-MS/ MS methods, co-elution of 2-AG with 1-AG, which is present in human serum, causes false 2-AG results. Conclusions: Our data highlight that the analytical specificity of MS/MS can be limited by interference from isobaric isomers with identical disintegration patterns. The specificity of this technology must be carefully evaluated for each individual application

An Astonishing Sixty Years: The Legacy of Hiroshima

Nobel Prize Lecture, December 8, 2005Game Theory; Conflict; Cooperation

Schelling segregation in an open city: a kinetically constrained Blume-Emery-Griffiths spin-1 system

In the 70's Schelling introduced a multi-agent model to describe the segregation dynamics that may occur with individuals having only weak preferences for 'similar' neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city-lattice. This model is directly related to the zero-temperature dynamics of the Blume-Emery-Griffiths (BEG) spin-1 model, with kinetic constraints. With a varying vacancy density, the dynamics with agents making deterministic decisions leads to a new variety of "phases" whose main features are the characteristics of the interfaces between clusters of agents of different types. The domains of existence of each type of interface are obtained analytically as well as numerically. These interfaces may completely isolate the agents leading to another type of segregation as compared to what is observed in the original Schelling model, and we discuss its possible socio-economic correlates.Comment: 10 pages, 7 figures, final version accepted for publication in PR

On ‘common-sense ontology’:A comment on the paper by Frank Hindriks and Francesco Guala

This note comments on Hindriks and Guala’s ‘unified theory of institutions’. One of the components that Hindriks and Guala seek to unify, and which they claim is unsatisfactory on its own, is the analysis of conventions that derives from the work of Lewis. I argue that the Lewisian approach provides simple and powerful explanations of many regularities in the social behaviour of humans and other animals. Those explanations can be seen as good social science even if, as Hindriks and Guala argue, they do not fit with common-sense ontology