Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: American option of stochastic volatility model with negative Fichera
  function on degenerate boundary   In this paper we study a general framework of American put option with
stochastic volatility whose value function is associated with a 2-dimensional
parabolic variational inequality with degenerate boundaries. We apply PDE
methods to analyze the existences of the strong solution and the properties of
the 2-dimensional manifold for the free boundary. Thanks to the regularity
result on the solution of the underlying PDE, we can also provide the
uniqueness of the solution by the argument of the verification theorem together
with the generalized Ito's formula even though the solution may not be second
order differentiable in the space variable across the free boundary.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph