16,102 research outputs found
Wealth-Driven Competition in a Speculative Financial Market: Examples with Maximizing Agents
This paper demonstrates how both quantitative and qualitative results of general, analytically tractable asset-pricing model in which heterogeneous agents behave consistently with a constant relative risk aversion assumption can be applied to the particular case of ``linear'' investment choices. In this way it is shown how the framework developed in Anufriev and Bottazzi (2005) can be used inside the classical setting with demand derived from utility maximization. Consequently, some of the previous contributions of the agent-based literature are generalized. In the course of the analysis of asymptotic market behavior the main attention is paid to a geometric approach which allows to visualize all possible equilibria by means of a simple one-dimensional curve referred as the Equilibrium Market Line. The case of linear (particularly, mean-variance) investment functions thoroughly analyzed in this paper allows to highlight those features of the asymptotic dynamics which are common to all types of the CRRA-investment behavior and those which are specific for the linear investment functions.Asset Pricing Model, CRRA Framework, Equilibrium Market Line, Rational Choice, Expected Utility Maximization, Mean-Variance Optimization, Linear Investment Functions.
Valuative analysis of planar plurisubharmonic functions
We show that valuations on the ring R of holomorphic germs in dimension 2 may
be naturally evaluated on plurisubharmonic functions, giving rise to
generalized Lelong numbers in the sense of Demailly. Any plurisubharmonic
function thus defines a real-valued function on the set V of valuations on R
and--by way of a natural Laplace operator defined in terms of the tree
structure on V--a positive measure on V. This measure contains a great deal of
information on the singularity at the origin. Under mild regularity
assumptions, it yields an exact formula for the mixed Monge-Ampere mass of two
plurisubharmonic functions. As a consequence, any generalized Lelong number can
be interpreted as an average of valuations. Using our machinery we also show
that the singularity of any positive closed (1,1) current T can be attenuated
in the following sense: there exists a finite composition of blowups such that
the pull-back of T decomposes into two parts, the first associated to a divisor
with normal crossing support, the second having small Lelong numbers.Comment: Final version. To appear in Inventiones Math. 37 pages, 5 figure
Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
We present an efficient procedure for computing resonances and resonant modes
of Helmholtz problems posed in exterior domains. The problem is formulated as a
nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use
of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains.
We consider a variational formulation and show that the spectrum consists of
isolated eigenvalues of finite multiplicity that only can accumulate at
infinity. The proposed method is based on a high order finite element
discretization combined with a specialization of the Tensor Infinite Arnoldi
method. Using Toeplitz matrices, we show how to specialize this method to our
specific structure. In particular we introduce a pole cancellation technique in
order to increase the radius of convergence for computation of eigenvalues that
lie close to the poles of the matrix-valued function. The solution scheme can
be applied to multiple resonators with a varying refractive index that is not
necessarily piecewise constant. We present two test cases to show stability,
performance and numerical accuracy of the method. In particular the use of a
high order finite element discretization together with TIAR results in an
efficient and reliable method to compute resonances
Likelihood Analysis of Power Spectra and Generalized Moment Problems
We develop an approach to spectral estimation that has been advocated by
Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance
extension problem, by Enqvist and Karlsson. The aim is to determine the power
spectrum that is consistent with given moments and minimizes the relative
entropy between the probability law of the underlying Gaussian stochastic
process to that of a prior. The approach is analogous to the framework of
earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a
generalization of the classical work by Burg and Jaynes on the maximum entropy
method. In the present paper we present a new fast algorithm in the general
case (i.e., for general Gaussian priors) and show that for priors with a
specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure
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