Jump processes

Ects : 6

Enseignant responsable :

  • JULIEN POISAT

Volume horaire : 18

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.