Gambling for resurrection and the heat equation on a triangle

Stefan Ankirchner (), Christophette Blanchet-Scalliet (), Nabil Kazi-Tani () and Chao Zhou ()
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Stefan Ankirchner: Friedrich-Schiller-Universität = Friedrich Schiller University Jena [Jena, Germany]
Christophette Blanchet-Scalliet: ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique
Nabil Kazi-Tani: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Chao Zhou: NUS - National University of Singapore

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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.

Keywords: Hitting probability; Stochastic control; Heat equation (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-sea
Note: View the original document on HAL open archive server: https://hal.science/hal-02405853v1
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Published in Applied Mathematics and Optimization, 2021, 84, pp.3111-3136. ⟨10.1007/s00245-020-09741-9⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02405853

DOI: 10.1007/s00245-020-09741-9

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