Degenerate backward SPDEs in bounded domains and applications to barrier options

Nikolai Dokuchaev

doi:10.3934/dcds.2015.35.5317

Article Contents

2015, Volume 35, Issue 11: 5317-5334. Doi: 10.3934/dcds.2015.35.5317

This issue Previous Article Backward doubly stochastic differential equations with polynomial growth coefficients Next Article On forward and backward SPDEs with non-local boundary conditions

Degenerate backward SPDEs in bounded domains and applications to barrier options

Nikolai Dokuchaev^1,

1.
Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, Western Australia, 6845

Received: August 31, 2013

Revised: April 30, 2014

Published: October 2015

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Abstract

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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Mathematics Subject Classification: Primary: 60J55, 60J60, 60H10, 91G20, 91G80; Secondary: 34F05.

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