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    On degenerate backward SPDEs in bounded domains under non-local conditions

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    Authors
    Dokuchaev, Nikolai
    Date
    2018
    Type
    Journal Article
    
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    Citation
    Dokuchaev, N. 2018. On degenerate backward SPDEs in bounded domains under non-local conditions. Stochastics: An International Journal of Probability of Probability and Stochastic Processes.
    Source Title
    Stochastics: An International Journal of Probability of Probability and Stochastic Processes
    DOI
    10.1080/17442508.2018.1480024
    ISSN
    1744-2508
    School
    School of Electrical Engineering, Computing and Mathematical Science (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/69100
    Collection
    • Curtin Research Publications
    Abstract

    The paper studies backward stochastic partial differential equations (BSPDEs) of parabolic type in bounded domains in the setting where the coercivity condition is not necessary satisfied and under special non-local in time and space boundary conditions replacing the standard Cauchy condition. These conditions connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability, and regularity results are obtained. As an example of applications, it is shown that degenerate BSPDEs with non-local boundary conditions arise naturally in modelling of portfolio selection problems, including models where dividend payoffs and management fees are taken into account.

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