These Lecture Notes are based on a course given in June 2001 at the Cattedra Galileiana of Scuola Normale Superiore di Pisa. The course consisted of a short introduction into the basic concepts of Mathematical Finance, focusing on the notion of ???no arbitrage???, and subsequently applying these concepts to portfolio optimization. To avoid technical difficulties I mainly dealt with the situation where the underlying probability space is finite and only sketched the difficulties arising in the general case. We then pass to the scheme of utility optimisation for general semi-martingale...
These Lecture Notes are based on a course given in June 2001 at the Cattedra Galileiana of Scuola Normale Superiore di Pisa. The course consisted of&n...
The lectures concentrate on some old and new relations between quasiderivatives of solutions to Ito stochastic equations and interior smoothness of harmonic functions associated with degenerate elliptic equations. Recent progress in the case of constant coefficients is discussed in full detail.
The lectures concentrate on some old and new relations between quasiderivatives of solutions to Ito stochastic equations and interior smoothness of ha...
This is a written version of the Cattedra Galileiana lectures, presented in 2002 at the Scuola Normale in Pisa. The objective is to combine an orientation to credit-risk modeling (emphasizing the valuation of corporate debt and credit derivatives) with an introduction to the analytical tractability and richness of affine state processes. This is not a general survey of either topic, but rather is designed to introduce researchers with some background in mathematics to a useful set of modeling techniques and an interesting set of applications.
This is a written version of the Cattedra Galileiana lectures, presented in 2002 at the Scuola Normale in Pisa. The objective is to combine an orienta...
The notes are based on lectures on stochastic processes given at Scuola Normale Superiore in 1999 and 2000. Some new material was added and only selected, less standard results were presented. We did not include several applications to statistical mechanics and mathematical finance, covered in the lectures, as we hope to write part two of the notes devoted to applications of stochastic processes in modelling. The main themes of the notes are constructions of stochastic processes. We present different approaches to the existence question proposed by Kolmogorov, Wiener, Ito and Prohorov....
The notes are based on lectures on stochastic processes given at Scuola Normale Superiore in 1999 and 2000. Some new material was added and only selec...
The achievement of Bose-Einstein condensation in ultra-cold vapours of alkali atoms has given enormous impulse to the study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. High purity and easy optical access make them ideal candidates to investigate fundamental issues on interacting quantum systems. This review presents some theoretical issues which have been addressed in this area and the numerical techniques which have been developed and used to describe them, from mean-field models to classical and quantum simulations for equilibrium and...
The achievement of Bose-Einstein condensation in ultra-cold vapours of alkali atoms has given enormous impulse to the study of dilute atomic gases in ...
This study provides innovative mathematical models for assessing the eruption probability and associated volcanic hazards, and applies them to the Campi Flegrei caldera in Italy.
This study provides innovative mathematical models for assessing the eruption probability and associated volcanic hazards, and applies them to the Cam...
This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds.
The local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates.
In dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to...
This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in hig...
This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi inPisa, on May 18-22, 2015.
This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematic...
