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

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.

KEYWORDS:

• Parabolic SPDEs
• backward SPDEs
• degenerate SPDEs
• SPDEs in domains
• non-local conditions
• portfolio selection

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by Australian Research Council grant of Australia DP120100928.