Analysis of PDEs and Applications to Stochastic Control
I am interested in the mathematical analysis of parabolic variational inequalities with free boundaries. My work primarily involves establishing existence, uniqueness, and regularity results for the solution of optimal control problems. I employ analytical tools (such as the penalty method) to address finite-horizon decision-making problems
Free Boundary & Obstacle Problems
I investigate the regularity and structural properties of free boundaries that arise in parabolic variational inequalities. A key contribution of my work is establishing the local Lipschitz continuity of free boundaries within this framework.
Optimal Stopping
I explore optimal stopping problems linked to utility maximization, where the agent makes irreversible decisions (like early retirement) based on path-dependent constraints.