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Article Dans Une Revue Applied Mathematics and Optimization Année : 2021

Gambling for resurrection and the heat equation on a triangle

Résumé

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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Dates et versions

hal-02405853 , version 1 (11-12-2019)

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Stefan Ankirchner, Christophette Blanchet-Scalliet, Nabil Kazi-Tani, Chao Zhou. Gambling for resurrection and the heat equation on a triangle. Applied Mathematics and Optimization, 2021, 84, pp.3111-3136. ⟨10.1007/s00245-020-09741-9⟩. ⟨hal-02405853⟩
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