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Gambling for resurrection and the heat equation on a triangle

Abstract : We consider the problem of controlling the diffusion coefficient of a diffusion with constant negative drift rate such that the probability of hitting a given lower barrier up to some finite time horizon is minimized. We assume that the diffusion rate can be chosen in a progressively measurable way with values in the interval [0, 1]. We prove that the value function is regular, concave in the space variable, and that it solves the associated HJB equation. To do so, we show that the heat equation on a right triangle, with a boundary condition that is discontinuous in the corner, possesses a smooth solution.
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https://hal.archives-ouvertes.fr/hal-02405853
Contributor : Nabil Kazi-Tani <>
Submitted on : Wednesday, December 11, 2019 - 8:52:26 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:26 PM
Long-term archiving on: : Thursday, March 12, 2020 - 10:53:05 PM

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Ankirchner, Blanchet-Scalliet,...
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  • HAL Id : hal-02405853, version 1

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Stefan Ankirchner, Christophette Blanchet-Scalliet, Nabil Kazi-Tani, Chao Zhou. Gambling for resurrection and the heat equation on a triangle. 2019. ⟨hal-02405853⟩

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