Degenerate backward SPDEs in domains: non-local boundary conditions and applications to finance

TL;DR

This paper investigates degenerate backward stochastic PDEs in bounded domains with non-local boundary conditions, establishing existence, uniqueness, and regularity results, and applying these findings to finance portfolio optimization.

Contribution

It introduces generalized solutions for degenerate backward SPDEs with non-local boundary conditions, expanding the theoretical framework and applications in finance.

Findings

Existence and uniqueness of solutions under degenerate conditions

Regularity results for solutions with non-local boundary conditions

Application to portfolio selection problems in finance

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 and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a standard Cauchy condition at the terminal time, problems with special non-local boundary conditions are considered. These non-local conditions connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability and regularity results are obtained. Some applications to portfolio selection problem are considered.