Year: 2020
Type: preprint
Abstract: In this paper, we derive sufficient and necessary maximum principles for a stochastic optimal control problem where the system state is given by a controlled stochastic differential equation with default. We prove existence of a unique solution to the controlled default stochastic differential equation. Furthermore, we prove existence and uniqueness of solution to the adjoint backward stochastic differential equation which appears in connection to the maximum principles. Finally, we apply the maximum principles to solve a utility maximisation problem with logarithmic utility functions.
Source: arXiv (Cornell University)
Institutions: Linnaeus University, University of Oslo
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2997849973