ETD

• ottimizzation
• Sobolev
• Stocastic

This thesis aims to study dynamic optimization problems for stochastic processes using the formalism of Sobolev spaces. In particular, it analyzes the existence, uniqueness, and regularity properties of solutions to the Hamilton–Jacobi–Bellman equations associated with controllable stochastic systems, explaining their connection with stochastic differential equations (SDEs) and possible applications in finance