Bjørn Kjær

Bjørn Kjær is a Senior Research Associate in the Stochastic Analysis and Control Division at the Institute for Advanced Dynamic Uncertainty. He holds a PhD in Mathematics from Aarhus University, where he was affiliated with the MaPhySto Centre for Mathematical Physics and Stochastics, and his doctoral research developed new results in the fluctuation theory of Lévy processes with two-sided exits. His thesis obtained explicit Wiener-Hopf factorisation identities for a class of spectrally asymmetric Lévy processes and derived closed-form expressions for first-passage distributions and overshoots, extending classical results due to Rogozin and Pecherskii to models with both diffusion and infinite-activity jump components.

Kjær's research centres on the structural theory of Lévy processes and its applications to problems in stochastic control and mathematical finance. He has worked on the potential theory of subordinators, the fine properties of local times for processes with jumps, and the asymptotic behaviour of Lévy processes conditioned to stay positive. A persistent concern in his work is the interplay between the Lévy–Khintchine triplet and the qualitative behaviour of the process — in particular, how the shape of the Lévy measure governs regularity of the scale function, oscillatory behaviour near the boundary, and the geometry of the resolvent kernel.

At IADU, his research addresses optimal stopping and singular control problems driven by Lévy noise, the construction of viscosity solution frameworks for integro-differential HJB equations with unbounded jump kernels, and Lévy-driven models for optimal liquidation and execution in illiquid markets.