Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov
  Processes   Drawdown (resp. drawup) of a stochastic process, also referred as the
reflected process at its supremum (resp. infimum), has wide applications in
many areas including financial risk management, actuarial mathematics and
statistics. In this paper, for general time-homogeneous Markov processes, we
study the joint law of the first passage time of the drawdown (resp. drawup)
process, its overshoot, and the maximum of the underlying process at this first
passage time. By using short-time pathwise analysis, under some mild regularity
conditions, the joint law of the three drawdown quantities is shown to be the
unique solution to an integral equation which is expressed in terms of
fundamental two-sided exit quantities of the underlying process. Explicit forms
for this joint law are found when the Markov process has only one-sided jumps
or is a L\'{e}vy process (possibly with two-sided jumps). The proposed
methodology provides a unified approach to study various drawdown quantities
for the general class of time-homogeneous Markov processes.

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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: math
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph