Approximation of non-Lipschitz SDEs by Picard iterations

Julien Baptiste (1, 2) , Julien Grepat (2) , Emmanuel Lépinette (2, 1)

1 PSL - Université Paris Sciences et Lettres
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper, we propose an approximation method based on Picard iterations deduced from the Doléans–Dade exponential formula. Our method allows to approximate trajectories of Markov processes in a large class, e.g. solutions to non-Lipchitz SDEs. An application to the pricing of Asian-style contingent claims in the CEV model is presented and compared to other methods of the literature.

Domaines: Probabilités [math.PR]

Julien Baptiste, Julien Grepat, Emmanuel Lépinette. Approximation of non-Lipschitz SDEs by Picard iterations. Applied Mathematical Finance, 2018, 25(2018) (2), pp.148-179. ⟨hal-01397399v2⟩