Abstract
As an important application of BSDEs and FBSDEs, in this chapter we present a classical method of the Stochastic Control Theory, the stochastic maximum principle, the main technical tool in this book. We first present stochastic control of BSDEs and then much more complex stochastic control of FBSDEs. Necessary conditions are obtained in terms of appropriate adjoint processes, which, under some conditions, can be characterized in terms of an FBSDE system. Sufficient conditions are stated in terms of the corresponding Hamiltonian function. Similar results are presented also for the case of the so-called weak formulation, in which the agent controls the distribution of the output process.
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Cvitanić, J., Zhang, J. (2013). Stochastic Maximum Principle. In: Contract Theory in Continuous-Time Models. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14200-0_10
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DOI: https://doi.org/10.1007/978-3-642-14200-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14199-7
Online ISBN: 978-3-642-14200-0
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