22,453 research outputs found
Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact
This paper is a continuation of Ishitani and Kato (2015), in which we derived
a continuous-time value function corresponding to an optimal execution problem
with uncertain market impact as the limit of a discrete-time value function.
Here, we investigate some properties of the derived value function. In
particular, we show that the function is continuous and has the semigroup
property, which is strongly related to the Hamilton-Jacobi-Bellman
quasi-variational inequality. Moreover, we show that noise in market impact
causes risk-neutral assessment to underestimate the impact cost. We also study
typical examples under a log-linear/quadratic market impact function with
Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648
The Mott insulator - 10th order perturbation theory extended to infinite order using QMC
We present a new method, based on the combination of analytical and numerical
techniques within the framework of the dynamical mean-field theory (DMFT).
Building upon numerically exact results obtained in an improved quantum Monte
Carlo (QMC) scheme, 10th order strong-coupling perturbation theory for the
Hubbard model on the Bethe lattice is extrapolated to infinite order. We obtain
continuous estimates of energy E and double occupancy D with unprecedented
precision O(10^{-5}) for the Mott insulator above its stability edge
U_{c1}=4.78 as well as critical exponents. The relevance for recent experiments
on Cr-doped V_2O_3 is pointed out.Comment: 4 pages, 5 figures. Significant changes in introduction and summary;
experimental reference added; Figs. 1 and 3 modifie
Comment on the equivalence of Bakamjian-Thomas mass operators in different forms of dynamics
We discuss the scattering equivalence of the generalized Bakamjian-Thomas
construction of dynamical representations of the Poincar\'e group in all of
Dirac's forms of dynamics. The equivalence was established by Sokolov in the
context of proving that the equivalence holds for models that satisfy cluster
separability. The generalized Bakamjian Thomas construction is used in most
applications, even though it only satisfies cluster properties for systems of
less than four particles. Different forms of dynamics are related by unitary
transformations that remove interactions from some infinitesimal generators and
introduce them to other generators. These unitary transformation must be
interaction dependent, because they can be applied to a non-interacting
generator and produce an interacting generator. This suggests that these
transformations can generate complex many-body forces when used in many-body
problems. It turns out that this is not the case. In all cases of interest the
result of applying the unitary scattering equivalence results in
representations that have simple relations, even though the unitary
transformations are dynamical. This applies to many-body models as well as
models with particle production. In all cases no new many-body operators are
generated by the unitary scattering equivalences relating the different forms
of dynamics. This makes it clear that the various calculations used in
applications that emphasize one form of the dynamics over another are
equivalent. Furthermore, explicit representations of the equivalent dynamical
models in any form of dynamics are easily constructed. Where differences do
appear is when electromagnetic probes are treated in the one-photon exchange
approximation. This approximation is different in each of Dirac's forms of
dynamics.Comment: 6 pages, no figure
Inviscid incompressible limits of the full Navier-Stokes-Fourier system
We consider the full Navier-Stokes-Fourier system in the singular limit for
the small Mach and large Reynolds and Peclet numbers, with ill prepared initial
data on the three dimensional Euclidean space. The Euler-Boussinesq
approximation is identified as the limit system
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