Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Indefinite linear-quadratic optimal control of mean-field stochastic
  differential equation with jump diffusion: an equivalent cost functional
  method   In this paper, we consider a linear-quadratic optimal control problem of
mean-field stochastic differential equation with jump diffusion, which is also
called as an MF-LQJ problem. Here, cost functional is allowed to be indefinite.
We use an equivalent cost functional method to deal with the MF-LQJ problem
with indefinite weighting matrices. Some equivalent cost functionals enable us
to establish a bridge between indefinite and positive-definite MF-LQJ problems.
With such a bridge, solvabilities of stochastic Hamiltonian system and Riccati
equations are further characterized. Optimal control of the indefinite MF-LQJ
problem is represented as a state feedback via solutions of Riccati equations.
As a by-product, the method provides a new way to prove the existence and
uniqueness of solution to mean field forward-backward stochastic differential
equation with jump diffusion (MF-FBSDEJ, for short), where existing methods in
literature do not work. Some examples are provided to illustrate our results.

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The categories of this paper are: acc-phys
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The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an