Petar Šimunović

Petar Šimunović completed his doctorate at the Faculty of Science of the University of Zagreb, where his dissertation developed convergence theory for sample average approximation (SAA) methods applied to infinite-dimensional stochastic programs. The work addressed the theoretical gap between finite-dimensional SAA analysis — where compactness arguments are available — and infinite-dimensional settings arising from stochastic control and PDE-constrained optimisation, establishing almost sure convergence and rate results under measurability and uniform integrability conditions on the objective integrand. The dissertation also treated the stability of optimal solution sets under perturbations to the sample size and the underlying probability measure, deriving quantitative bounds in terms of Wasserstein distance between the true and empirical distributions. He subsequently held a postdoctoral fellowship at the Department of Mathematics of the Università degli Studi di Milano, where he worked on distributionally robust optimisation and the duality theory of minimax problems over ambiguity sets.

Following the postdoctoral period, Šimunović investigated distributionally robust optimisation (DRO) over Wasserstein balls, establishing strong duality results and tractable equivalent reformulations for a class of convex loss functions. The duality analysis connected DRO to the theory of coherent risk measures — specifically to the Conditional Value-at-Risk and its robust extensions — and yielded finite-dimensional convex programmes that can be solved efficiently when the nominal distribution is a finite empirical measure. A companion programme developed stochastic gradient methods for risk-averse optimisation problems with Conditional Value-at-Risk objectives, establishing convergence rates in both the smooth and non-smooth cases and analysing the variance of gradient estimators under heavy-tailed loss distributions.

At IADU, Šimunović contributes stochastic and robust optimisation theory to the Institute's research on decision-making under uncertainty in sovereign and central banking settings. His work examines optimal portfolio allocation for sovereign wealth funds under distributional ambiguity, robust reserve management formulations for central banks, and the connection between DRO frameworks and the ambiguity-averse optimal control problems that arise in the Hamilton-Jacobi-Bellman setting under Knightian uncertainty.