Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coupled continuous time random walks in finance   Continuous time random walks (CTRWs) are used in physics to model anomalous
diffusion, by incorporating a random waiting time between particle jumps. In
finance, the particle jumps are log-returns and the waiting times measure delay
between transactions. These two random variables (log-return and waiting time)
are typically not independent. For these coupled CTRW models, we can now
compute the limiting stochastic process (just like Brownian motion is the limit
of a simple random walk), even in the case of heavy tailed (power-law) price
jumps and/or waiting times. The probability density functions for this limit
process solve fractional partial differential equations. In some cases, these
equations can be explicitly solved to yield descriptions of long-term price
changes, based on a high-resolution model of individual trades that includes
the statistical dependence between waiting times and the subsequent
log-returns. In the heavy tailed case, this involves operator stable space-time
random vectors that generalize the familiar stable models. In this paper, we
will review the fundamental theory and present two applications with
tick-by-tick stock and futures data.

29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat