Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perpetual American options in diffusion-type models with running maxima
  and drawdowns   We study perpetual American option pricing problems in an extension of the
Black-Merton-Scholes model in which the dividend and volatility rates of the
underlying risky asset depend on the running values of its maximum and maximum
drawdown. The optimal exercise times are shown to be the first times at which
the underlying asset hits certain boundaries depending on the running values of
the associated maximum and maximum drawdown processes. We obtain closed-form
solutions to the equivalent free-boundary problems for the value functions with
smooth fit at the optimal stopping boundaries and normal reflection at the
edges of the state space of the resulting three-dimensional Markov process. The
optimal exercise boundaries for the perpetual American options on the maximum
of the market depth with fixed and floating strikes are determined as the
minimal solutions of certain first-order nonlinear ordinary differential
equations.

7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin