|via A. M. Ampère 56 - 20131 Milano (Italy)|
1) An overview of Levy processes
(infinitely divisible laws, Levy-Khintchine formula, structure of the jumps, Markov property and applications, some path properties).
2) Some aspect of subordinators
(Levy-Khintchine-Ito's theory on $R_+$, examples, Bochner's subordination, renewal theory in continuous times).
3) Levy processes with no negative jumps
(extrema of Levy processes with no negative jumps, connection with subordinators, formulas of fluctuation theory, connection with branching processes).
4) Exponential functionals
(method of moments for the law of the exponential functional of a subordinator, case of general Levy processes, connection with self-similar Markov processes, Stieltjes' problem of moments).
5) Some aspects of Levy processes in mathematical finance and
(models with jumps, stochastic volatility, ruin problem,...).