Journal
OPTIMAL CONTROL APPLICATIONS & METHODS
Volume 42, Issue 3, Pages 833-847Publisher
WILEY
DOI: 10.1002/oca.2705
Keywords
forward-backward stochastic differential equation; mean-field; mixed deterministic and random control; optimal control
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Funding
- National Natural Science Foundation of China [61633015, 61821004]
- National Natural Science Fund for Distinguished Young Scholars of China [61925306]
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This paper focuses on a mixed optimal control problem driven by forward-backward stochastic differential equation, discussing necessary and sufficient conditions, as well as solving a linear-quadratic mixed optimal control problem. The theoretical results are applied to solve a problem of information security investment and cyber insurance.
This paper is concerned with a mixed optimal control problem driven by forward-backward stochastic differential equation, where the term mixed means that there are two controllers, one is a deterministic controller and the other is a random controller. We derive a necessary condition and a sufficient condition for the mixed optimal control problem. A linear-quadratic mixed optimal control problem is discussed, and the corresponding optimal control is expressed by the solution of mean-field forward-backward stochastic differential equation. A feature here is that we obtain a mean-field forward-backward stochastic differential equation, which naturally arises from the study of mixed optimal control problem driven by forward-backward stochastic differential equation without mean-field term. As an application of theoretical results obtained here, we solve a problem of information security investment and cyber insurance.
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