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arXiv · 2611.09428

Kolmogorov Obstacle Problems: Euclidean Free Boundary Regularity under a Cone Condition

Junkee Jeon·Takwon Kim·Jehan Oh
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Abstract

We study obstacle problems for Kolmogorov-type operators that diffuse in one variable and transport in another. Such problems describe American options on running averages. Under a cone estimate, a strong monotonicity condition on the solution in the diffusive direction, we show that the free boundary is a graph in the diffusive direction with Hölder continuous first derivatives in the Euclidean sense, and that every free boundary point is regular. The key observation is that a Euclidean Lipschitz free boundary is flat at the intrinsic scale. For the American fixed-strike Asian option we verify the cone estimate, so that its exercise boundary has the same regularity.

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Junkee Jeon, Takwon Kim, Jehan Oh. 2026-11-06. Kolmogorov Obstacle Problems: Euclidean Free Boundary Regularity under a Cone Condition. https://arxiv.org/abs/2611.09428

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