9 research outputs found
Hydrodynamics in an external field
The methods of statistical dynamics are applied to a fluid with 5 conserved
fields (the mass, the energy, and the three components of momentum) moving in a
given external potential. When the potential is zero, we recover a previously
derived system of parabolic differential equations, called "corrections to
fluid dynamics".Comment: extends results of math-ph/0105013 in the presence of an external
field; to appear in Rep. Math. Phys. (2002
The quantum information manifold for epsilon-bounded forms
Let H be a self-adjoint operator bounded below by 1, and let V be a small
form perturbation such that RVS has finite norm, where R is the resolvent at
zero to the power 1/2 +epsilon, and S is the resolvent to the power
1/2-epsilon. Here, epsilon lies between 0 and 1/2. If the Gibbs state defined
by H is sufficiently regular, we show that the free energy is an analytic
function of V in the sense of Frechet, and that the family of density operators
defined in this way is an analytic manifold modelled on a Banach space.Comment: 12 pages, report to Torun Conference, 199
A Hedged Monte Carlo Approach to Real Option Pricing
In this work we are concerned with valuing optionalities associated to invest
or to delay investment in a project when the available information provided to
the manager comes from simulated data of cash flows under historical (or
subjective) measure in a possibly incomplete market. Our approach is suitable
also to incorporating subjective views from management or market experts and to
stochastic investment costs. It is based on the Hedged Monte Carlo strategy
proposed by Potters et al (2001) where options are priced simultaneously with
the determination of the corresponding hedging. The approach is particularly
well-suited to the evaluation of commodity related projects whereby the
availability of pricing formulae is very rare, the scenario simulations are
usually available only in the historical measure, and the cash flows can be
highly nonlinear functions of the prices.Comment: 25 pages, 14 figure
Nonparametric Information Geometry
The differential-geometric structure of the set of positive densities on a
given measure space has raised the interest of many mathematicians after the
discovery by C.R. Rao of the geometric meaning of the Fisher information. Most
of the research is focused on parametric statistical models. In series of
papers by author and coworkers a particular version of the nonparametric case
has been discussed. It consists of a minimalistic structure modeled according
the theory of exponential families: given a reference density other densities
are represented by the centered log likelihood which is an element of an Orlicz
space. This mappings give a system of charts of a Banach manifold. It has been
observed that, while the construction is natural, the practical applicability
is limited by the technical difficulty to deal with such a class of Banach
spaces. It has been suggested recently to replace the exponential function with
other functions with similar behavior but polynomial growth at infinity in
order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give
first a review of our theory with special emphasis on the specific issues of
the infinite dimensional setting. In a second part we discuss two specific
topics, differential equations and the metric connection. The position of this
line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30
2013 Pari