Ioannis Drakos

Ioannis Drakos is a Senior Research Associate in the Optimal Policy and Applications Division at the Institute for Advanced Dynamic Uncertainty. He holds a PhD in Mathematics from King's College London (Department of Mathematics), where his doctoral research developed sharp regularity results for the free boundary in a class of optimal stopping problems driven by multidimensional diffusions. His thesis established continuous differentiability of the exercise boundary under general drift and diffusion coefficients, extended the smooth-fit principle to settings with state-dependent volatility and killing rates, and derived the first rigorous local-time decomposition for the value function at the free boundary in problems with non-smooth payoffs.

Drakos's research centres on the fine properties of free boundaries arising in optimal stopping and singular stochastic control: the regularity of the boundary as a function of the model parameters, the rate of convergence of numerical approximations to the true boundary, and the qualitative behaviour of the value function in the vicinity of contact. He has particular interest in problems where the free boundary exhibits non-monotone or disconnected structure — settings in which classical one-dimensional intuition fails and where a genuinely multidimensional stochastic analysis is required. His work draws heavily on potential theory, the theory of excessive functions, and probabilistic representations of solutions to elliptic and parabolic PDEs.

At IADU, his research focuses on free boundary problems embedded in HJB equations for policy optimisation, optimal intervention timing for a regulator facing a controlled diffusion with irreversible state transitions, and the analysis of contact sets in mean field game systems where the equilibrium density develops singular support.