Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic maximum principle, dynamic programming principle, and their
  relationship for fully coupled forward-backward stochastic control systems   Within the framework of viscosity solution, we study the relationship between
the maximum principle (MP) in [9] and the dynamic programming principle (DPP)
in [10] for a fully coupled forward-backward stochastic controlled system
(FBSCS) with a nonconvex control domain. For a fully coupled FBSCS, both the
corresponding MP and the corresponding Hamilton-Jacobi-Bellman (HJB) equation
combine an algebra equation respectively. So this relationship becomes more
complicated and almost no work involves this issue. With the help of a new
decoupling technique, we obtain the desirable estimates for the fully coupled
forward-backward variational equations and establish the relationship.
Furthermore, for the smooth case, we discover the connection between the
derivatives of the solution to the algebra equation and some terms in the first
and second-order adjoint equations. Finally, we study the local case under the
monotonicity conditions as in [14,27] and obtain the relationship between the
MP in [27] and the DPP in [14].

10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph