Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Introducing and solving generalized Black-Scholes PDEs through the use
  of functional calculus   We introduce some families of generalized Black--Scholes equations which
involve the Riemann-Liouville and Weyl space-fractional derivatives. We prove
that these generalized Black--Scholes equations are well-posed in
$(L^1-L^\infty)$-interpolation spaces. More precisely, we show that the
elliptic type operators involved in these equations generate holomorphic
semigroups. Then, we give explicit integral expressions for the associated
solutions. In the way to obtain well-posedness, we prove a new connection
between bisectorial operators and sectorial operators in an abstract setting.
Such a connection extends some known results in the topic to a wider family of
both operators and the functions involved.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc