ECTS : 6
Description du contenu de l'enseignement :
Relationship between conditional expectations and parabolic linear PDEs.
Formulation of standard stochastic control problems: dynamic programming principle.
Hamilton-Jacobi-Bellman equation
Verification approach
Viscosity solutions (definitions, existence, comparison)
Application to portfolio management, optimal shutdown and switching problems
Teacher : Bruno BOUCHARD
Compétence à acquérir :
PDEs and stochastic control problems naturally arise in risk control, option pricing, calibration, portfolio management, optimal book liquidation, etc. The aim of this course is to study the associated techniques, in particular to present the notion of viscosity solutions for PDEs.