Density Forecast of Financial Returns Using Decomposition and Maximum Entropy

We consider a multiplicative decomposition of the financial returns to improve the density forecasts of financial returns. The multiplicative decomposition is based on the identity that financial return is the product of its absolute value and its sign. Advantages of modeling the two components are discussed. To reduce the effect of the estimation error due to the multiplicative decomposition in estimation of the density forecast model, we impose a moment constraint that the conditional mean forecast is set to match with the sample mean. Imposing such a moment constraint operates a shrinkage and tilts the density forecast of the decomposition model to produce the improved maximum entropy density forecast. An empirical application to forecasting density of the daily stock returns demonstrates the benefits of using the decomposition and imposing the moment constraint to obtain the improved density forecast. We evaluate the density forecast by comparing the logarithmic score (LS), the quantile score (QS), and the continuous ranked probability score (CRPS). We contribute to the literature on the density forecast and the decomposition models by showing that the density forecast of the decomposition model can be improved by imposing a sensible constraint in the maximum entropy framework.

Angular momentum and parity projected multidimensionally constrained relativistic Hartree-Bogoliubov model

The nuclear deformations are of fundamental importance in nuclear physics. Recently we developed a multi-dimensionally constrained relativistic Hartree-Bogoliubov (MDCRHB) model, in which all multipole deformations respecting the $V_4$ symmetry can be considered self-consistently. In this work we extend this model by incorporating the angular momentum projection (AMP) and parity projection (PP) to restore the rotational and parity symmetries broken in the mean-field level. This projected-MDCRHB (p-MDCRHB) model enables us to connect certain nuclear spectra to exotic intrinsic shapes such as triangle or tetrahedron. We present the details of the method and an exemplary calculation for $^{12}$C. We develop a triangular moment constraint to generate the triangular configurations consisting of three $\alpha$ clusters arranged as an equilateral triangle. The resulting $^{12}$C spectra are consistent with that from a triangular rigid rotor for large separations between the $\alpha$ clusters. We also calculate the $B(E2)$ and $B(E3)$ values for low-lying states and find good agreement with the experiments.

Global constraints in modeling and solving problems within the Constraint Programming paradigm.

At the moment, constraint programming technology is a powerful tool for solving combinatorial search and combinatorial optimization problems. To use this technology, any task must be formulated as a task of satisfying constraints. The role of the concept of global constraints in modeling and solving applied problems within the framework of the constraint programming paradigm can hardly be overestimated. The procedures that implement the algorithms of filtering global constraints are the elementary “building blocks” from which the model of a specific applied problem is built. Algorithms for filtering global constraints, as a rule, are supported by the corresponding developed theories that allow organizing high-performance computing. The choice of a particular software library is primarily determined by the extent to which the set and method of implementing global constraints corresponds tothe level of modern research in this area. The main focus of this article is focused on an overview of global constraints that are implemented within the most popular constraint programming libraries: Choco, GeCode, JaCoP, MiniZinc.

A Two-Moment Inequality with Applications to Rényi Entropy and Mutual Information

This paper explores some applications of a two-moment inequality for the integral of the rth power of a function, where 0<r<1. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. More generally, evaluation of the bound with two carefully chosen nonzero moments can lead to significant improvements with a modest increase in complexity. The second contribution is a method for upper bounding mutual information in terms of certain integrals with respect to the variance of the conditional density. The bounds have a number of useful properties arising from the connection with variance decompositions.

A Maximum Entropy Approach for Uncertainty Quantification and Analysis of Multifunctional Materials

The Maximum Entropy (ME) method is shown to provide a new approach for quantifying model uncertainty in the presence of complex, heterogeneous data. This is important in model validation of a variety of multifunctional constitutive relations. For example, multifunctional materials contain field-coupled material parameters that should be self-consistent regardless of the measurement. A classical example is piezoelectricity which may be quantified from charge induced by stress or strain induced by an electric field. The proposed tools provide new statistical information to address measurement discrepancies, guide model development, and catalyze materials discovery for data fusion problems. The error between the model outputs and heterogeneous data is quantified and used to formulate a second moment constraint within the entropy functional. This leads to an augmented likelihood function that weights each individual set of data by its respective variance and covariance between each data set. As a first step, the method is evaluated on a piezoelectric ceramic to illustrate how the covariance matrix influences piezoelectric parameter estimation from heterogeneous electric displacement and strain data.

Moment classification of infinite energy solutions to the homogeneous Boltzmann equation

In this paper, we will introduce a precise classification of characteristic functions in the Fourier space according to the moment constraint in the physical space of any order. Based on this, we construct measure-valued solutions to the homogeneous Boltzmann equation with the exact moment condition as the initial data.

Discrete-Time Indefinite Stochastic Linear Quadratic Optimal Control with Second Moment Constraints

This paper studies the discrete-time stochastic linear quadratic (LQ) problem with a second moment constraint on the terminal state, where the weighting matrices in the cost functional are allowed to be indefinite. By means of the matrix Lagrange theorem, a new class of generalized difference Riccati equations (GDREs) is introduced. It is shown that the well-posedness, and the attainability of the LQ problem and the solvability of the GDREs are equivalent to each other.