Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovery of time dependent volatility coefficient by linearization   We study the problem of reconstruction of special special time dependent
local volatility from market prices of options with different strikes at two
expiration times. For a general diffusion process we apply the linearization
technique and we conclude that the option price can be obtained as the sum of
the Black-Scholes formula and of an operator $W$ which is linear in
perturbation of volatility. We further simplify the linearized inverse problem
and obtain unique solvability result in basic functional spaces. By using the
Laplace transform in time we simplify the kernels of integral operators for $W$
and we obtain uniqueness and stability results for for volatility under natural
condition of smallness of the spacial interval where one prescribes the
(market) data. We propose a numerical algorithm based on our analysis of the
linearized problem.

0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph