Confronto tra sistemi trend following e mean reversion

Si descrivono strategie di trading trend following e strategie mean reversion applicate a vari strumenti finanziari

Mean curvature flow in SE (2) and applications to visual perception

Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Limiting theorems in statistical mechanics. The mean-field case.

The Curie-Weiss model is defined by ah Hamiltonian according to spins interact. For some particular values of the parameters, the sum of the spins normalized with square-root normalization converges or not toward Gaussian distribution. In the thesis we investigate some correlations between the behaviour of the sum and the central limit for interacting random variables.

L'approccio di Trading mean reverting evidenze statistiche

Analisi di una strategia di trading mean reverting al fine di valutare la fattibilita del suo utilizzo intraday nel mercato telematico azionario italiano. Panoramica sui sistemi di meccanizzazione algoritmica e approfondimento sull'HFT.