Global regularity and probabilistic schemes for free boundary surfaces of multivariate American derivatives and their Greeks

In a rather general setting of multivariate stochastic volatility market models we derive global iterative probabilistic schemes for computing the free boundary and its Greeks for a generic class of American derivative models using front-fixing methods. Convergence is closely linked to a proof of global regularity of the free boundary surface

Maximal parabolic regularity for divergence operators including mixed boundary conditions

We show that elliptic second order operators $A$ of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of $A$ are discontinuous and $A$ is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth data are presented.Comment: 39 pages, 4 postscript figure