ECTS : 6
Description du contenu de l'enseignement :
Poisson process, compound Poisson process,
Infinitely divisible distributions,
Random measures of Poisson,
Lévy process,
Decomposition of Lévy-Khintchine,
Itô's formula for Lévy processes,
Stochastic differential equations driven by a Lévy process,
Equivalence of measures, Doleans-Dade exponential, Girsanov's theorem
Merton’s Model
Hawkes' Process
Compétence à acquérir :
This course aims to master the techniques of analysis and stochastic calculation specific to jump processes. It complements the "Stochastic Calculation" course which is limited to processes with continuous paths.