1,861 research outputs found
Application of the Kelly Criterion to Ornstein-Uhlenbeck Processes
In this paper, we study the Kelly criterion in the continuous time framework
building on the work of E.O. Thorp and others. The existence of an optimal
strategy is proven in a general setting and the corresponding optimal wealth
process is found. A simple formula is provided for calculating the optimal
portfolio for a set of price processes satisfying some simple conditions.
Properties of the optimal investment strategy for assets governed by multiple
Ornstein-Uhlenbeck processes are studied. The paper ends with a short
discussion of the implications of these ideas for financial markets.Comment: presented at Complex'2009 (Shanghai, Feb. 23-25
Consumption processes and positively homogeneous projection properties
We constructively prove the existence of time-discrete consumption processes
for stochastic money accounts that fulfill a pre-specified positively
homogeneous projection property (PHPP) and let the account always be positive
and exactly zero at the end. One possible example is consumption rates forming
a martingale under the above restrictions. For finite spaces, it is shown that
any strictly positive consumption strategy with restrictions as above possesses
at least one corresponding PHPP and could be constructed from it. We also
consider numeric examples under time-discrete and -continuous account
processes, cases with infinite time horizons and applications to income
drawdown and bonus theory.Comment: 24 pages, 2 figure
Optimal consumption and investment with bounded downside risk for power utility functions
We investigate optimal consumption and investment problems for a
Black-Scholes market under uniform restrictions on Value-at-Risk and Expected
Shortfall. We formulate various utility maximization problems, which can be
solved explicitly. We compare the optimal solutions in form of optimal value,
optimal control and optimal wealth to analogous problems under additional
uniform risk bounds. Our proofs are partly based on solutions to
Hamilton-Jacobi-Bellman equations, and we prove a corresponding verification
theorem. This work was supported by the European Science Foundation through the
AMaMeF programme.Comment: 36 page
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
A Note on the Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection
According to the Smoluchowski-Kramers approximation, the solution of the
equation
converges to the solution of the equation
as {\mu}->0. We consider here
a similar result for the Langevin process with elastic reflection on the
boundary.Comment: 14 pages, 2 figure
Models of Passive and Reactive Tracer Motion: an Application of Ito Calculus
By means of Ito calculus it is possible to find, in a straight-forward way,
the analytical solution to some equations related to the passive tracer
transport problem in a velocity field that obeys the multidimensional Burgers
equation and to a simple model of reactive tracer motion.Comment: revised version 7 pages, Latex, to appear as a letter to J. of
Physics
First-passage theory of exciton population loss in single-walled carbon nanotubes reveals micron-scale intrinsic diffusion lengths
One-dimensional crystals have long range translational invariance which
manifests as long exciton diffusion lengths, but such intrinsic properties are
often obscured by environmental perturbations. We use a first-passage approach
to model single-walled carbon nanotube (SWCNT) exciton dynamics (including
exciton-exciton annihilation and end effects) and compare it to results from
both continuous-wave and multi-pulse ultrafast excitation experiments to
extract intrinsic SWCNT properties. Excitons in suspended SWCNTs experience
macroscopic diffusion lengths, on the order of the SWCNT length, (1.3-4.7 um)
in sharp contrast to encapsulated samples. For these pristine samples, our
model reveals intrinsic lifetimes (350-750 ps), diffusion constants (130-350
cm^2/s), and absorption cross-sections (2.1-3.6 X 10^-17 cm^2/atom) among the
highest previously reported.and diffusion lengths for SWCNTs.Comment: 6 pages, 3 figure
Motion in a Random Force Field
We consider the motion of a particle in a random isotropic force field.
Assuming that the force field arises from a Poisson field in , , and the initial velocity of the particle is sufficiently large, we
describe the asymptotic behavior of the particle
Diffusions with rank-based characteristics and values in the nonnegative quadrant
We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not both. The construction involves solving a system of coupled Skorokhod reflection equations, then "unfolding" the Skorokhod reflection of a suitable semimartingale in the manner of Prokaj (Statist. Probab. Lett. 79 (2009) 534-536). Questions of pathwise uniqueness and strength are also addressed, for systems of stochastic differential equations with reflection that realize these diffusions. When the variance of the laggard is at least as large as that of the leader, it is shown that the corner of the quadrant is never visited
Normal forms approach to diffusion near hyperbolic equilibria
We consider the exit problem for small white noise perturbation of a smooth
dynamical system on the plane in the neighborhood of a hyperbolic critical
point. We show that if the distribution of the initial condition has a scaling
limit then the exit distribution and exit time also have a joint scaling limit
as the noise intensity goes to zero. The limiting law is computed explicitly.
The result completes the theory of noisy heteroclinic networks in two
dimensions. The analysis is based on normal forms theory.Comment: 21 page
- …