8,228 research outputs found
Modulated Information Flows in Financial Markets
We model continuous-time information flows generated by a number of
information sources that switch on and off at random times. By modulating a
multi-dimensional L\'evy random bridge over a random point field, our framework
relates the discovery of relevant new information sources to jumps in
conditional expectation martingales. In the canonical Brownian random bridge
case, we show that the underlying measure-valued process follows jump-diffusion
dynamics, where the jumps are governed by information switches. The dynamic
representation gives rise to a set of stochastically-linked Brownian motions on
random time intervals that capture evolving information states, as well as to a
state-dependent stochastic volatility evolution with jumps. The nature of
information flows usually exhibits complex behaviour, however, we maintain
analytic tractability by introducing what we term the effective and
complementary information processes, which dynamically incorporate active and
inactive information, respectively. As an application, we price a financial
vanilla option, which we prove is expressed by a weighted sum of option values
based on the possible state configurations at expiry. This result may be viewed
as an information-based analogue of Merton's option price, but where
jump-diffusion arises endogenously. The proposed information flows also lend
themselves to the quantification of asymmetric informational advantage among
competitive agents, a feature we analyse by notions of information geometry.Comment: 27 pages, 1 figur
Stability Optimization of Positive Semi-Markov Jump Linear Systems via Convex Optimization
In this paper, we study the problem of optimizing the stability of positive
semi-Markov jump linear systems. We specifically consider the problem of tuning
the coefficients of the system matrices for maximizing the exponential decay
rate of the system under a budget-constraint. By using a result from the matrix
theory on the log-log convexity of the spectral radius of nonnegative matrices,
we show that the stability optimization problem reduces to a convex
optimization problem under certain regularity conditions on the system matrices
and the cost function. We illustrate the validity and effectiveness of the
proposed results by using an example from the population biology
Superdiffusive heat conduction in semiconductor alloys -- II. Truncated L\'evy formalism for experimental analysis
Nearly all experimental observations of quasi-ballistic heat flow are
interpreted using Fourier theory with modified thermal conductivity. Detailed
Boltzmann transport equation (BTE) analysis, however, reveals that the
quasi-ballistic motion of thermal energy in semiconductor alloys is no longer
Brownian but instead exhibits L\'evy dynamics with fractal dimension . Here, we present a framework that enables full 3D experimental analysis by
retaining all essential physics of the quasi-ballistic BTE dynamics
phenomenologically. A stochastic process with just two fitting parameters
describes the transition from pure L\'evy superdiffusion as short length and
time scales to regular Fourier diffusion. The model provides accurate fits to
time domain thermoreflectance raw experimental data over the full modulation
frequency range without requiring any `effective' thermal parameters and
without any a priori knowledge of microscopic phonon scattering mechanisms.
Identified values for InGaAs and SiGe match ab initio BTE predictions
within a few percent. Our results provide experimental evidence of fractal
L\'evy heat conduction in semiconductor alloys. The formalism additionally
indicates that the transient temperature inside the material differs
significantly from Fourier theory and can lead to improved thermal
characterization of nanoscale devices and material interfaces
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