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Sharp Estimates for Geman–Yor Processes and applications to Arithmetic Average Asian options
- Source :
- Journal de Mathématiques Pures et Appliquées. 129:87-130
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 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.
- Subjects :
- Hypoelliptic operators
Pointwise
Harnack inequality
Partial differential equation
Stochastic process
Geman–Yor stochastic process
Optimal control
Mathematics (all)
Applied Mathematics
General Mathematics
010102 general mathematics
01 natural sciences
010101 applied mathematics
Fundamental solution
Applied mathematics
Asian option
0101 mathematics
Invariant (mathematics)
Mathematics
Harnack's inequality
Subjects
Details
- ISSN :
- 00217824
- Volume :
- 129
- Database :
- OpenAIRE
- Journal :
- Journal de Mathématiques Pures et Appliquées
- Accession number :
- edsair.doi.dedup.....ec3e3d4e5ab6b10f20e861d0b127c5ac