A new moment matching algorithm for sampling from partially specified symmetric distributions

A new algorithm is proposed for generating scenarios from a partially specified symmetric multivariate distribution. The algorithm generates samples which match the first two moments exactly and match the marginal fourth moments approximately, using a semidefinite programming procedure. The performance of the algorithm is illustrated by a numerical example

An algorithm for moment-matching scenario generation with application to financial portfolio optimization

We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimisation example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments)

Demand uncertainty In modelling WDS: scaling laws and scenario generation

Water distribution systems (WDS) are critical infrastructures that should be designed to work properly in different conditions. The design and management of WDS should take into account the uncertain nature of some system parameters affecting the overall reliability of these infrastructures. In this context, water demand represents the major source of uncertainty. Thus, uncertain demand should be either modelled as a stochastic process or characterized using statistical tools. In this paper, we extend to the 3rd and 4th order moments the analytical equations (namely scaling laws) expressing the dependency of the statistical moments of demand signals on the sampling time resolution and on the number of served users. Also, we describe how the probability density function (pdf) of the demand signal changes with both the increase of the user’s number and the sampling rate variation. With this aim, synthetic data and real indoor water demand data are used. The scaling laws of the water demand statistics are a powerful tool which allows us to incorporate the demand uncertainty in the optimization models for a sustainable management of WDS. Specifically, in the stochastic/robust optimization, solutions close to the optimum in different working conditions should be considered. Obviously, the results of these optimization models are strongly dependent on the conditions that are taken into consideration (i.e. the scenarios). Among the approaches for the definition of demand scenarios and their probability-weight of occurrence, the moment-matching method is based on matching a set of statistical properties, e.g. moments from the 1st (mean) to the 4th (kurtosis) order

Domestic energy management methodology for optimizing efficiency in Smart Grids

Increasing energy prices and the greenhouse effect lead to more awareness of energy efficiency of electricity supply. During the last years, a lot of domestic technologies have been developed to improve this efficiency. These technologies on their own already improve the efficiency, but more can be gained by a combined management. Multiple optimization objectives can be used to improve the efficiency, from peak shaving and Virtual Power Plant (VPP) to adapting to fluctuating generation of wind turbines. In this paper a generic management methology is proposed applicable for most domestic technologies, scenarios and optimization objectives. Both local scale optimization objectives (a single house) and global scale optimization objectives (multiple houses) can be used. Simulations of different scenarios show that both local and global objectives can be reached

Resonance frequency and radiative Q-factor of plasmonic and dielectric modes of small objects

The electromagnetic scattering resonances of a non-magnetic object much smaller than the incident wavelength in vacuum can be either described by the electroquasistatic approximation of the Maxwell's equations if its permittivity is negative, or by the magnetoquasistatic approximation if its permittivity is positive and sufficiently high. Nevertheless, these two approximations fail to correctly account for the frequency shift and the radiative broadening of the resonances when the size of the object becomes comparable to the wavelength of operation. In this manuscript, the radiation corrections to the electroquasistatic and magnetoquasistatic resonances of arbitrarily-shaped objects are derived, which only depend on the quasistatic current modes. Then, closed form expressions of the frequency-shift and the radiative Q-factor of both plasmonic and dielectric modes of small objects are introduced, where the dependencies on the material and the size of the object are factorized. In particular, it is shown that the radiative Q-factor explicitly depends on the multipolar components of the quasistatic modes

Linear and nonlinear filtering in mathematical finance: a review

Copyright @ The Authors 2010This paper presents a review of time series filtering and its applications in mathematical finance. A summary of results of recent empirical studies with market data are presented for yield curve modelling and stochastic volatility modelling. The paper also outlines different approaches to filtering of nonlinear time series