Degenerate backward SPDEs in bounded domains and applications to barrier options
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Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied. Generalized solutions based on the representation theorem are suggested. Some regularity is derived from the regularity of the first exit times of non-Markov characteristic processes. Uniqueness, solvability and regularity results are obtained. Applications to pricing and hedging of European barrier options are considered.
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Dokuchaev, Nikolai (2011)The representation theorem is obtained for functionals of non-Markov processes and their first exit times from bounded domains. These functionals are represented via solutions of backward parabolic Ito equations. As an ...
Dokuchaev, Nikolai (2015)We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that ...
Dokuchaev, Nikolai (2010)We study existence, uniqueness, semi-group property, and a priori estimates for solutions for backward parabolic Ito equations in domains with boundary. We study also duality between forward and backward equations. The ...