Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic control for a class of nonlinear kernels and applications   We consider a stochastic control problem for a class of nonlinear kernels.
More precisely, our problem of interest consists in the optimisation, over a
set of possibly non-dominated probability measures, of solutions of backward
stochastic differential equations (BSDEs). Since BSDEs are nonlinear
generalisations of the traditional (linear) expectations, this problem can be
understood as stochastic control of a family of nonlinear expectations, or
equivalently of nonlinear kernels. Our first main contribution is to prove a
dynamic programming principle for this control problem in an abstract setting,
which we then use to provide a semi-martingale characterisation of the value
function. We next explore several applications of our results. We first obtain
a wellposedness result for second order BSDEs (as introduced in [86]) which
does not require any regularity assumption on the terminal condition and the
generator. Then we prove a nonlinear optional decomposition in a robust
setting, extending recent results of [71], which we then use to obtain a
super-hedging duality in uncertain, incomplete and nonlinear financial markets.
Finally, we relate, under additional regularity assumptions, the value function
to a viscosity solution of an appropriate path-dependent partial differential
equation (PPDE).

19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th