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Vecer derived a degenerate parabolic equation with a boundary conditioncharacterizing the price of Asian options with generally sampled average. It iswell understood that there exists a unique probabilistic solution to such aproblem but it remained unclear whether the probabilistic solution is aclassical solution. We prove that the probabilistic solutions to Vecer's PDEare regular.

Regularity of a degenerate parabolic equation appearing in Vecer's unified pricing of Asian options