3,285 research outputs found
A queueing theory description of fat-tailed price returns in imperfect financial markets
In a financial market, for agents with long investment horizons or at times
of severe market stress, it is often changes in the asset price that act as the
trigger for transactions or shifts in investment position. This suggests the
use of price thresholds to simulate agent behavior over much longer timescales
than are currently used in models of order-books.
We show that many phenomena, routinely ignored in efficient market theory,
can be systematically introduced into an otherwise efficient market, resulting
in models that robustly replicate the most important stylized facts.
We then demonstrate a close link between such threshold models and queueing
theory, with large price changes corresponding to the busy periods of a
single-server queue. The distribution of the busy periods is known to have
excess kurtosis and non-exponential decay under various assumptions on the
queue parameters. Such an approach may prove useful in the development of
mathematical models for rapid deleveraging and panics in financial markets, and
the stress-testing of financial institutions
Markov-modulated Brownian motion with two reflecting barriers
We consider a Markov-modulated Brownian motion reflected to stay in a strip
[0,B]. The stationary distribution of this process is known to have a simple
form under some assumptions. We provide a short probabilistic argument leading
to this result and explaining its simplicity. Moreover, this argument allows
for generalizations including the distribution of the reflected process at an
independent exponentially distributed epoch. Our second contribution concerns
transient behavior of the reflected system. We identify the joint law of the
processes t,X(t),J(t) at inverse local times.Comment: 13 pages, 1 figur
Stabilization of an overloaded queueing network using measurement-based admission control
Admission control can be employed to avoid congestion in queueing networks
subject to overload. In distributed networks the admission decisions are often
based on imperfect measurements on the network state. This paper studies how
the lack of complete state information affects the system performance by
considering a simple network model for distributed admission control. The
stability region of the network is characterized and it is shown how feedback
signaling makes the system very sensitive to its parameters.Comment: Published at http://dx.doi.org/10.1239/jap/1143936256 in the Journal
of Applied Probability (http://projecteuclid.org/jap) by the Applied
Probability Trust (http://www.appliedprobability.org/
Validity of heavy traffic steady-state approximations in generalized Jackson Networks
We consider a single class open queueing network, also known as a generalized
Jackson network (GJN). A classical result in heavy-traffic theory asserts that
the sequence of normalized queue length processes of the GJN converge weakly to
a reflected Brownian motion (RBM) in the orthant, as the traffic intensity
approaches unity. However, barring simple instances, it is still not known
whether the stationary distribution of RBM provides a valid approximation for
the steady-state of the original network. In this paper we resolve this open
problem by proving that the re-scaled stationary distribution of the GJN
converges to the stationary distribution of the RBM, thus validating a
so-called ``interchange-of-limits'' for this class of networks. Our method of
proof involves a combination of Lyapunov function techniques, strong
approximations and tail probability bounds that yield tightness of the sequence
of stationary distributions of the GJN.Comment: Published at http://dx.doi.org/10.1214/105051605000000638 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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