The Anglo-French defence partnership after the “Brexit” vote: new incentives and new dilemmas

Since the signing of the Lancaster House Treaties in 2010, the bilateral partnership between Paris and London has been a key axis for both countries’ involvement in Europe’s security and defence affairs. What impact can the result of the “Brexit” vote have on this rising partnership? This contribution argues that while the partnership will undoubtedly remain central in Europe, the two parties will in the future both face contradictory incentives. While London will have new incentives to invest in its relationship with Paris, it might also try to discourage further defence integration in the EU. On the contrary, France – which had been more forward leaning, and concerned with Britain’s lack of commitment to a bilateral relationship they considered central – will be tempted to look elsewhere. Indeed, the ambition for a militarily active European Union with a strong defence industrial base may prove contradictory with an investment in the bilateral partnership with London

Limit theorems for non-Markovian and fractional processes

This thesis examines various non-Markovian and fractional processes---rough volatility models, stochastic Volterra equations, Wiener chaos expansions---through the prism of asymptotic analysis. Stochastic Volterra systems serve as a conducive framework encompassing most rough volatility models used in mathematical finance. In Chapter 2, we provide a unified treatment of pathwise large and moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhiraja, Dupuis and Ellis. This powerful approach also enables us to investigate the pathwise large deviations of families of white noise functionals characterised by their Wiener chaos expansion as~$X^\varepsilon = \sum_{n=0}^{\infty} \varepsilon^n I_n \big(f_n^{\varepsilon} \big).$ In Chapter 3, we provide sufficient conditions for the large deviations principle to hold in path space, thereby refreshing a problem left open By Pérez-Abreu (1993). Hinging on analysis on Wiener space, the proof involves describing, controlling and identifying the limit of perturbed multiple stochastic integrals. In Chapter 4, we come back to mathematical finance via the route of Malliavin calculus. We present explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European options on a stock and VIX options. In particular, we develop a detailed analysis of the two-factor rough Bergomi model. Finally, in Chapter 5, we consider the large-time behaviour of affine stochastic Volterra equations, an under-developed area in the absence of Markovianity. We leverage on a measure-valued Markovian lift introduced by Cuchiero and Teichmann and the associated notion of generalised Feller property. This setting allows us to prove the existence of an invariant measure for the lift and hence of a stationary distribution for the affine Volterra process, featuring in the rough Heston model.Open Acces