Stochastic invariance of closed sets with non-Lipschitz coefficients

Eduardo Abi Jaber (1) , Bruno Bouchard (1) , Camille Illand (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 AXA Investment Managers, Multi Asset Client Solutions, Quantitative Research

This paper provides a new characterization of the stochastic invariance of a closed subset of R^d with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can fail to be differentiable: we only assume that the covariance matrix is. In particular, our result can be directly applied to construct affine diffusions and polynomial preserving diffusions on any arbitrary closed set.

Mots clés: affine diffusions; polynomial preserving diffusions; stochastic invariance; Stochastic differential equation

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

Eduardo Abi Jaber, Bruno Bouchard, Camille Illand. Stochastic invariance of closed sets with non-Lipschitz coefficients. 2016. ⟨hal-01349639v2⟩