123 research outputs found
The obstacle problem for semilinear parabolic partial integro-differential equations
This paper presents a probabilistic interpretation for the weak Sobolev
solution of the obstacle problem for semilinear parabolic partial
integro-differential equations (PIDEs).
The results of Leandre (1985) concerning the homeomorphic property for the
solution of SDEs with jumps are used to construct random test functions for the
variational equation for such PIDEs. This results in the natural connection
with the associated Reflected Backward Stochastic Differential Equations with
jumps (RBSDEs), namely Feynman Kac's formula for the solution of the PIDEs.
Moreover it gives an application to the pricing and hedging of contingent
claims with constraints in the wealth or portfolio processes in financial
markets including jumps.Comment: 31 page
Existence and uniqueness results for BSDEs with jumps: the whole nine yards
This paper is devoted to obtaining a wellposedness result for
multidimensional BSDEs with possibly unbounded random time horizon and driven
by a general martingale in a filtration only assumed to satisfy the usual
hypotheses, i.e. the filtration may be stochastically discontinuous. We show
that for stochastic Lipschitz generators and unbounded, possibly infinite, time
horizon, these equations admit a unique solution in appropriately weighted
spaces. Our result allows in particular to obtain a wellposedness result for
BSDEs driven by discrete--time approximations of general martingales.Comment: 48 pages, final version, forthcoming in the Electronic Journal of
Probabilit
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