73 research outputs found
The Exact Value for European Options on a Stock Paying a Discrete Dividend
In the context of a Black-Scholes economy and with a no-arbitrage argument,
we derive arbitrarily accurate lower and upper bounds for the value of European
options on a stock paying a discrete dividend. Setting the option price error
below the smallest monetary unity, both bounds coincide, and we obtain the
exact value of the option.Comment: 14 pages,3 figure
Equilibrium price dynamics in an overlapping-generations exchange economy
We present a continuous time overlapping generations model for an endowment Arrow-Debreu economy with an age-structured popu¬lation. For an economy with a balanced growth path, we prove that Arrow-Debreu equilibrium prices exist, and their dynamic properties are age-dependent. Our model allows for an explicit dependence of prices on critical age-specific endowment parameters. We show that, if endowments are distributed earlier than some critical age, then spec¬ulative bubbles for prices do exist
Synchronization of Huygens' clocks and the Poincare method
We study two models of connected pendulum clocks synchronizing their
oscillations, a phenomenon originally observed by Huygens. The oscillation
angles are assumed to be small so that the pendulums are modeled by harmonic
oscillators, clock escapements are modeled by the van der Pol terms. The mass
ratio of the pendulum bobs to their casings is taken as a small parameter.
Analytic conditions for existence and stability of synchronization regimes, and
analytic expressions for their stable amplitudes and period corrections are
derived using the Poincare theorem on existence of periodic solutions in
autonomous quasi-linear systems. The anti-phase regime always exists and is
stable under variation of the system parameters. The in-phase regime may exist
and be stable, exist and be unstable, or not exist at all depending on
parameter values. As the damping in the frame connecting the clocks is
increased the in-phase stable amplitude and period are decreasing until the
regime first destabilizes and then disappears. The results are most complete
for the traditional three degrees of freedom model, where the clock casings and
the frame are consolidated into a single mass.Comment: 23 pages, 8 figure
A Software Tool to Model Genetic Regulatory Networks. Applications to the Modeling of Threshold Phenomena and of Spatial Patterning in Drosophila
We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by the Mathematica software package GeneticNetworks. This package accepts as input the interaction graphs of the transcriptional activators and repressors of a biological process and, as output, gives the mathematical model in the form of a system of ordinary differential equations. All the relevant biological parameters are chosen automatically by the software. Within this framework, we show that concentration dependent threshold effects in biology emerge from the catalytic properties of genes and its associated conservation laws. We apply this methodology to the segment patterning in Drosophila early development and we calibrate the genetic transcriptional network responsible for the patterning of the gap gene proteins Hunchback and Knirps, along the antero-posterior axis of the Drosophila embryo. In this approach, the zygotically produced proteins Hunchback and Knirps do not diffuse along the antero-posterior axis of the embryo of Drosophila, developing a spatial pattern due to concentration dependent thresholds. This shows that patterning at the gap genes stage can be explained by the concentration gradients along the embryo of the transcriptional regulators
Stable Knotted Strings
We solve the Cauchy problem for the relativistic closed string in Minkowski
space , including the cases where the initial data has a knot like
topology. We give the general conditions for the world sheet of a closed
knotted string to be a time periodic surface. In the particular case of zero
initial string velocity the period of the world sheet is proportional to half
the length () of the initial string and a knotted string always collapses
to a link for . Relativistic closed strings are dynamically evolving
or pulsating structures in spacetime, and knotted or unknotted like structures
remain stable over time. The generation of arbitrary -fold knots, starting
with an initial simple link configuration with non zero velocity is possible.Comment: 15 pages, 4 figures, Plain Tex. Final version for Phys. Lett.
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