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.

Sharp Estimates for Geman–Yor Processes and applications to Arithmetic Average Asian options / Cibelli, Gennaro; Polidoro, Sergio; Rossi, Francesco. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 129:(2019), pp. 87-130. [10.1016/j.matpur.2018.12.009]

Sharp Estimates for Geman–Yor Processes and applications to Arithmetic Average Asian options

Cibelli, Gennaro
Membro del Collaboration Group
;
Polidoro, Sergio
Membro del Collaboration Group
;
2019

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.
2019
10-dic-2018
129
87
130
Sharp Estimates for Geman–Yor Processes and applications to Arithmetic Average Asian options / Cibelli, Gennaro; Polidoro, Sergio; Rossi, Francesco. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 129:(2019), pp. 87-130. [10.1016/j.matpur.2018.12.009]
Cibelli, Gennaro; Polidoro, Sergio; Rossi, Francesco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1169228
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