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- W2963341540 abstract "We prove the existence of the fundamental solution of the degenerate second order partial differential equation related to Geman–Yor stochastic processes, that arise in models for option pricing theory in finance. We then prove pointwise lower and upper bounds for such fundamental solution. Lower bounds are obtained by using repeatedly an invariant Harnack inequality and by solving an associated optimal control problem with quadratic cost. Upper bounds are obtained by the fact that the cost satisfies a specific Hamilton–Jacobi–Bellman equation. Nous démontrons l'existence de la solution fondamentale pour une equation différentielle dégénérée d'ordre deux associée au processus stochastique de Geman–Yor. Ce dernier est utilisé dans des modèles issus de la théorie du “pricing” des options financières. Nous obtenons ensuite des bornes ponctuelles inférieures et supérieures pour cette solution fondamentale. Les bornes inférieures sont obtenues en utilisant de faχcon répétée une inégalité de Harnack invariante et en résolvant un problème de commande optimale avec coût quadratique. Les bornes supérieures sont quant à elles dérivées en utilisant le fait que le coût satisfait une équation de Hamilton–Jacobi–Bellman." @default.
- W2963341540 created "2019-07-30" @default.
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- W2963341540 date "2019-09-01" @default.
- W2963341540 modified "2023-10-13" @default.
- W2963341540 title "Sharp Estimates for Geman–Yor Processes and applications to Arithmetic Average Asian options" @default.
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- W2963341540 doi "https://doi.org/10.1016/j.matpur.2018.12.009" @default.
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