32 research outputs found
Hedging in Field Theory Models of the Term Structure
We use path integrals to calculate hedge parameters and efficacy of hedging
in a quantum field theory generalization of the Heath, Jarrow and Morton (HJM)
term structure model which parsimoniously describes the evolution of
imperfectly correlated forward rates. We also calculate, within the model
specification, the effectiveness of hedging over finite periods of time. We use
empirical estimates for the parameters of the model to show that a low
dimensional hedge portfolio is quite effective.Comment: 18 figures, Invited Talk, International Econophysics Conference,
Bali, 28-31 August 200
Entropy and Uncertainty of Squeezed Quantum Open Systems
We define the entropy S and uncertainty function of a squeezed system
interacting with a thermal bath, and study how they change in time by following
the evolution of the reduced density matrix in the influence functional
formalism. As examples, we calculate the entropy of two exactly solvable
squeezed systems: an inverted harmonic oscillator and a scalar field mode
evolving in an inflationary universe. For the inverted oscillator with weak
coupling to the bath, at both high and low temperatures, , where r is
the squeeze parameter. In the de Sitter case, at high temperatures, where , being the coupling to the bath and H
the Hubble constant. These three cases confirm previous results based on more
ad hoc prescriptions for calculating entropy. But at low temperatures, the de
Sitter entropy is noticeably different. This result, obtained
from a more rigorous approach, shows that factors usually ignored by the
conventional approaches, i.e., the nature of the environment and the coupling
strength betwen the system and the environment, are important.Comment: 36 pages, epsfig, 2 in-text figures include
Thermal Particle Creation in Cosmological Spacetimes: A Stochastic Approach
The stochastic method based on the influence functional formalism introduced
in an earlier paper to treat particle creation in near-uniformly accelerated
detectors and collapsing masses is applied here to treat thermal and
near-thermal radiance in certain types of cosmological expansions. It is
indicated how the appearance of thermal radiance in different cosmological
spacetimes and in the two apparently distinct classes of black hole and
cosmological spacetimes can be understood under a unifying conceptual and
methodological framework.Comment: 17 pages, revtex (aps, eqsecnum), submitted to PRD, April 199
A New Theory of Stochastic Inflation
The stochastic inflation program is a framework for understanding the
dynamics of a quantum scalar field driving an inflationary phase. Though widely
used and accepted, there have over recent years been serious criticisms of this
theory. In this paper I will present a new theory of stochastic inflation which
avoids the problems of the conventional approach. Specifically, the theory can
address the quantum-to-classical transition problem, and it will be shown to
lead to a dramatic easing of the fine tuning constraints that have plagued
inflation theories.Comment: 28 pages in latex (uses revtex), no figures. Changes include 3 pages
of extra detail in the derivation of the noise and dissipation kernels, and a
more careful description of the approximations made. Results remain unchange