Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The general mixture-diffusion SDE and its relationship with an
  uncertain-volatility option model with volatility-asset decorrelation   In the present paper, given an evolving mixture of probability densities, we
define a candidate diffusion process whose marginal law follows the same
evolution. We derive as a particular case a stochastic differential equation
(SDE) admitting a unique strong solution and whose density evolves as a mixture
of Gaussian densities. We present an interesting result on the comparison
between the instantaneous and the terminal correlation between the obtained
process and its squared diffusion coefficient. As an application to
mathematical finance, we construct diffusion processes whose marginal densities
are mixtures of lognormal densities. We explain how such processes can be used
to model the market smile phenomenon. We show that the lognormal mixture
dynamics is the one-dimensional diffusion version of a suitable uncertain
volatility model, and suitably reinterpret the earlier correlation result. We
explore numerically the relationship between the future smile structures of
both the diffusion and the uncertain volatility versions.

35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con