Density analysis of non-Markovian BSDEs and applications to biology and finance

Thibaut Mastrolia (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL

In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in particular cases. We apply these results to both the study of a gene expression model in biology and to the classical pricing problems in mathematical finance.

Mots clés: BSDEs; Malliavin calculus; Nourdin-Viens' Formula; gene expression; option pricing

Domaines: Probabilités [math.PR]

Thibaut Mastrolia. Density analysis of non-Markovian BSDEs and applications to biology and finance. 2016. ⟨hal-01275679⟩