468 research outputs found
Optimal control of predictive mean-field equations and applications to finance
We study a coupled system of controlled stochastic differential equations
(SDEs) driven by a Brownian motion and a compensated Poisson random measure,
consisting of a forward SDE in the unknown process and a
\emph{predictive mean-field} backward SDE (BSDE) in the unknowns . The driver of the BSDE at time may depend not just upon the
unknown processes , but also on the predicted future
value , defined by the conditional expectation . \\ We give a sufficient and a necessary
maximum principle for the optimal control of such systems, and then we apply
these results to the following two problems:\\ (i) Optimal portfolio in a
financial market with an \emph{insider influenced asset price process.} \\ (ii)
Optimal consumption rate from a cash flow modeled as a geometric It\^ o-L\'
evy SDE, with respect to \emph{predictive recursive utility}
A maximum principle for infinite horizon delay equations
We prove a maximum principle of optimal control of stochastic delay equations
on infinite horizon. We establish first and second sufficient stochastic
maximum principles as well as necessary conditions for that problem. We
illustrate our results by an application to the optimal consumption rate from
an economic quantity
Normal Heat Conduction in a Chain with Weak Interparticle Anharmonic Potential
We analytically study heat conduction in a chain with interparticle
interaction V(x)=lambda[1-cos(x)] and harmonic on-site potential. We start with
each site of the system connected to a Langevin heat bath, and investigate the
case of small coupling for the interior sites in order to understand the
behavior of the system with thermal reservoirs at the boundaries only. We
study, in a perturbative analysis, the heat current in the steady state of the
one-dimensional system with weak interparticle potential. We obtain an
expression for the thermal conductivity, compare the low and high temperature
regimes, and show that, as we turn off the couplings with the interior heat
baths, there is a "phase transition:'' the Fourier's law holds only at high
temperatures
Non-equilibrium Statistical Mechanics of Anharmonic Crystals with Self-consistent Stochastic Reservoirs
We consider a d-dimensional crystal with an arbitrary harmonic interaction
and an anharmonic on-site potential, with stochastic Langevin heat bath at each
site. We develop an integral formalism for the correlation functions that is
suitable for the study of their relaxation (time decay) as well as their
behavior in space. Furthermore, in a perturbative analysis, for the
one-dimensional system with weak coupling between the sites and small quartic
anharmonicity, we investigate the steady state and show that the Fourier's law
holds. We also obtain an expression for the thermal conductivity (for arbitrary
next-neighbor interactions) and give the temperature profile in the steady
state
Precautionary Measures for Credit Risk Management in Jump Models
Sustaining efficiency and stability by properly controlling the equity to
asset ratio is one of the most important and difficult challenges in bank
management. Due to unexpected and abrupt decline of asset values, a bank must
closely monitor its net worth as well as market conditions, and one of its
important concerns is when to raise more capital so as not to violate capital
adequacy requirements. In this paper, we model the tradeoff between avoiding
costs of delay and premature capital raising, and solve the corresponding
optimal stopping problem. In order to model defaults in a bank's loan/credit
business portfolios, we represent its net worth by Levy processes, and solve
explicitly for the double exponential jump diffusion process and for a general
spectrally negative Levy process.Comment: 31 pages, 4 figure
Modeling temporal fluctuations in avalanching systems
We demonstrate how to model the toppling activity in avalanching systems by
stochastic differential equations (SDEs). The theory is developed as a
generalization of the classical mean field approach to sandpile dynamics by
formulating it as a generalization of Itoh's SDE. This equation contains a
fractional Gaussian noise term representing the branching of an avalanche into
small active clusters, and a drift term reflecting the tendency for small
avalanches to grow and large avalanches to be constricted by the finite system
size. If one defines avalanching to take place when the toppling activity
exceeds a certain threshold the stochastic model allows us to compute the
avalanche exponents in the continum limit as functions of the Hurst exponent of
the noise. The results are found to agree well with numerical simulations in
the Bak-Tang-Wiesenfeld and Zhang sandpile models. The stochastic model also
provides a method for computing the probability density functions of the
fluctuations in the toppling activity itself. We show that the sandpiles do not
belong to the class of phenomena giving rise to universal non-Gaussian
probability density functions for the global activity. Moreover, we demonstrate
essential differences between the fluctuations of total kinetic energy in a
two-dimensional turbulence simulation and the toppling activity in sandpiles.Comment: 14 pages, 11 figure
Deterministic Dicke state preparation with continuous measurement and control
We characterize the long-time projective behavior of the stochastic master
equation describing a continuous, collective spin measurement of an atomic
ensemble both analytically and numerically. By adding state based feedback, we
show that it is possible to prepare highly entangled Dicke states
deterministically.Comment: Additional information is available at
http://minty.caltech.edu/Ensemble
Gaussian approximation and single-spin measurement in OSCAR MRFM with spin noise
A promising technique for measuring single electron spins is magnetic
resonance force microscopy (MRFM), in which a microcantilever with a permanent
magnetic tip is resonantly driven by a single oscillating spin. If the quality
factor of the cantilever is high enough, this signal will be amplified over
time to the point that it can be detected by optical or other techniques. An
important requirement, however, is that this measurement process occur on a
time scale short compared to any noise which disturbs the orientation of the
measured spin. We describe a model of spin noise for the MRFM system, and show
how this noise is transformed to become time-dependent in going to the usual
rotating frame. We simplify the description of the cantilever-spin system by
approximating the cantilever wavefunction as a Gaussian wavepacket, and show
that the resulting approximation closely matches the full quantum behavior. We
then examine the problem of detecting the signal for a cantilever with thermal
noise and spin with spin noise, deriving a condition for this to be a useful
measurement.Comment: 12 pages, 8 figures in EPS format, RevTeX 4.
Pulsating Front Speed-up and Quenching of Reaction by Fast Advection
We consider reaction-diffusion equations with combustion-type non-linearities
in two dimensions and study speed-up of their pulsating fronts by general
periodic incompressible flows with a cellular structure. We show that the
occurence of front speed-up in the sense ,
with the amplitude of the flow and the (minimal) front speed, only
depends on the geometry of the flow and not on the reaction function. In
particular, front speed-up happens for KPP reactions if and only if it does for
ignition reactions. We also show that the flows which achieve this speed-up are
precisely those which, when scaled properly, are able to quench any ignition
reaction.Comment: 16p
Continuous quantum feedback of coherent oscillations in a solid-state qubit
We have analyzed theoretically the operation of the Bayesian quantum feedback
of a solid-state qubit, designed to maintain perfect coherent oscillations in
the qubit for arbitrarily long time. In particular, we have studied the
feedback efficiency in presence of dephasing environment and detector
nonideality. Also, we have analyzed the effect of qubit parameter deviations
and studied the quantum feedback control of an energy-asymmetric qubit.Comment: 11 page
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