345 research outputs found
Optimal hedging of Derivatives with transaction costs
We investigate the optimal strategy over a finite time horizon for a
portfolio of stock and bond and a derivative in an multiplicative Markovian
market model with transaction costs (friction). The optimization problem is
solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem
has well-behaved solutions if certain conditions on a potential are satisfied.
In the case at hand, these conditions simply imply arbitrage-free
("Black-Scholes") pricing of the derivative. While pricing is hence not changed
by friction allow a portfolio to fluctuate around a delta hedge. In the limit
of weak friction, we determine the optimal control to essentially be of two
parts: a strong control, which tries to bring the stock-and-derivative
portfolio towards a Black-Scholes delta hedge; and a weak control, which moves
the portfolio by adding or subtracting a Black-Scholes hedge. For simplicity we
assume growth-optimal investment criteria and quadratic friction.Comment: Revised version, expanded introduction and references 17 pages,
submitted to International Journal of Theoretical and Applied Finance (IJTAF
Behavior of heuristics and state space structure near SAT/UNSAT transition
We study the behavior of ASAT, a heuristic for solving satisfiability
problems by stochastic local search near the SAT/UNSAT transition. The
heuristic is focused, i.e. only variables in unsatisfied clauses are updated in
each step, and is significantly simpler, while similar to, walksat or Focused
Metropolis Search. We show that ASAT solves instances as large as one million
variables in linear time, on average, up to 4.21 clauses per variable for
random 3SAT. For K higher than 3, ASAT appears to solve instances at the ``FRSB
threshold'' in linear time, up to K=7.Comment: 12 pages, 6 figures, longer version available as MSc thesis of first
author at http://biophys.physics.kth.se/docs/ardelius_thesis.pd
Cooperative action in eukaryotic gene regulation: physical properties of a viral example
The Epstein-Barr virus (EBV) infects more than 90% of the human population,
and is the cause of several both serious and mild diseases. It is a
tumorivirus, and has been widely studied as a model system for gene
(de)regulation in human. A central feature of the EBV life cycle is its ability
to persist in human B cells in states denoted latency I, II and III. In latency
III the host cell is driven to cell proliferation and hence expansion of the
viral population, but does not enter the lytic pathway, and no new virions are
produced, while the latency I state is almost completely dormant. In this paper
we study a physico-chemical model of the switch between latency I and latency
III in EBV. We show that the unusually large number of binding sites of two
competing transcription factors, one viral and one from the host, serves to
make the switch sharper (higher Hill coefficient), either by cooperative
binding between molecules of the same species when they bind, or by competition
between the two species if there is sufficient steric hindrance.Comment: 7 pages, 6 figures, 1 tabl
Random pure Gaussian states and Hawking radiation
A black hole evaporates by Hawking radiation. Each mode of that radiation is
thermal. If the total state is nevertheless to be pure, modes must be
entangled. Estimating the minimum size of this entanglement has been an
important outstanding issue. We develop a new theory of constrained random
symplectic transformations, based on that the total state is pure and Gaussian
with given marginals. In the random constrained symplectic model we then
compute the distribution of mode-mode correlations, from which we bound
mode-mode entanglement. Modes of frequency much larger than are not populated at time and drop out of the analysis.
Among the other modes find that correlations and hence entanglement between
relatively thinly populated modes (early-time high-frequency modes and/or late
modes of any frequency) to be strongly suppressed. Relatively highly populated
modes (early-time low-frequency modes) can on the other hand be strongly
correlated, but a detailed analysis reveals that they are nevertheless also
weakly entangled. Our analysis hence establishes that restoring unitarity after
a complete evaporation of a black hole does not require strong quantum
entanglement between any pair of Hawking modes. Our analysis further gives
exact general expressions for the distribution of mode-mode correlations in
random, pure, Gaussian states with given marginals, which may have applications
beyond black hole physics.Comment: Revised version, with supplementary material. Main paper 6 pages, 3
figures. Supplementary material 29 pages, 1 figur
Experimental evidence of chaotic advection in a convective flow
Lagrangian chaos is experimentally investigated in a convective flow by means
of Particle Tracking Velocimetry. The Fnite Size Lyapunov Exponent analysis is
applied to quantify dispersion properties at different scales. In the range of
parameters of the experiment, Lagrangian motion is found to be chaotic.
Moreover, the Lyapunov depends on the Rayleigh number as . A
simple dimensional argument for explaining the observed power law scaling is
proposed.Comment: 7 pages, 3 figur
On the relationship between directed percolation and the synchronization transition in spatially extended systems
We study the nature of the synchronization transition in spatially extended
systems by discussing a simple stochastic model. An analytic argument is put
forward showing that, in the limit of discontinuous processes, the transition
belongs to the directed percolation (DP) universality class. The analysis is
complemented by a detailed investigation of the dependence of the first passage
time for the amplitude of the difference field on the adopted threshold. We
find the existence of a critical threshold separating the regime controlled by
linear mechanisms from that controlled by collective phenomena. As a result of
this analysis we conclude that the synchronization transition belongs to the DP
class also in continuous models. The conclusions are supported by numerical
checks on coupled map lattices too
Inference of kinetic Ising model on sparse graphs
Based on dynamical cavity method, we propose an approach to the inference of
kinetic Ising model, which asks to reconstruct couplings and external fields
from given time-dependent output of original system. Our approach gives an
exact result on tree graphs and a good approximation on sparse graphs, it can
be seen as an extension of Belief Propagation inference of static Ising model
to kinetic Ising model. While existing mean field methods to the kinetic Ising
inference e.g., na\" ive mean-field, TAP equation and simply mean-field, use
approximations which calculate magnetizations and correlations at time from
statistics of data at time , dynamical cavity method can use statistics of
data at times earlier than to capture more correlations at different time
steps. Extensive numerical experiments show that our inference method is
superior to existing mean-field approaches on diluted networks.Comment: 9 pages, 3 figures, comments are welcom
Predictability in Systems with Many Characteristic Times: The Case of Turbulence
In chaotic dynamical systems, an infinitesimal perturbation is exponentially
amplified at a time-rate given by the inverse of the maximum Lyapunov exponent
. In fully developed turbulence, grows as a power of the
Reynolds number. This result could seem in contrast with phenomenological
arguments suggesting that, as a consequence of `physical' perturbations, the
predictability time is roughly given by the characteristic life-time of the
large scale structures, and hence independent of the Reynolds number. We show
that such a situation is present in generic systems with many degrees of
freedom, since the growth of a non-infinitesimal perturbation is determined by
cumulative effects of many different characteristic times and is unrelated to
the maximum Lyapunov exponent. Our results are illustrated in a chain of
coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed
with uufile
Beyond inverse Ising model: structure of the analytical solution for a class of inverse problems
I consider the problem of deriving couplings of a statistical model from
measured correlations, a task which generalizes the well-known inverse Ising
problem. After reminding that such problem can be mapped on the one of
expressing the entropy of a system as a function of its corresponding
observables, I show the conditions under which this can be done without
resorting to iterative algorithms. I find that inverse problems are local (the
inverse Fisher information is sparse) whenever the corresponding models have a
factorized form, and the entropy can be split in a sum of small cluster
contributions. I illustrate these ideas through two examples (the Ising model
on a tree and the one-dimensional periodic chain with arbitrary order
interaction) and support the results with numerical simulations. The extension
of these methods to more general scenarios is finally discussed.Comment: 15 pages, 6 figure
Growth of non-infinitesimal perturbations in turbulence
We discuss the effects of finite perturbations in fully developed turbulence
by introducing a measure of the chaoticity degree associated to a given scale
of the velocity field. This allows one to determine the predictability time for
non-infinitesimal perturbations, generalizing the usual concept of maximum
Lyapunov exponent. We also determine the scaling law for our indicator in the
framework of the multifractal approach. We find that the scaling exponent is
not sensitive to intermittency corrections, but is an invariant of the
multifractal models. A numerical test of the results is performed in the shell
model for the turbulent energy cascade.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed
with uufile
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