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Quadratic Approximation (quadratic + approximation)

Distribution by Scientific Domains
Business, Economics, Finance and Accounting40%

Selected Abstracts

Quadratic form of stable sub-manifold for power systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9-10 2004
Daizhan Cheng
Abstract The stable sub-manifold of type-1 unstable equilibrium point is fundamental in determining the region of attraction of a stable working point for power systems, because such sub-manifolds form the boundary of the region (IEEE Trans. Automat. Control 1998; 33(1):16,27; IEEE Trans. Circuit Syst. 1988; 35(6):712,728). The quadratic approximation has been investigated in some recent literatures (Automatica 1997; 33(10):1877,1883; IEEE Trans. Power Syst. 1997; 12(2):797,802). First, the paper reports our recent result: a precise formula is obtained, which provides the unique quadratic approximation with the error of 0(,,x,,3). Then the result is applied to differential,algebraic systems. The real form of practical large scale power systems are of this type. A detailed algorithm is obtained for the quadratic approximation of the stable sub-manifold of type-1 unstable equilibrium points of such systems. Some examples are presented to illustrate the algorithm and the application of the approximation to stability analysis of power systems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Piecewise quadratic approximation of the non-dominated set for bi-criteria programs

JOURNAL OF MULTI CRITERIA DECISION ANALYSIS, Issue 1 2001
Margaret M. Wiecek
Abstract A procedure to approximate the non-dominated set for general (continuous) bi-criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighbourhood of a non-dominated point of interest and based on primal,dual relationships associated with the weighted Tchebycheff scalarization of the original problem. The approximating quadratic functions, in which decision maker's preferences are represented, give a closed-form description of the non-dominated set. A numerical example is included. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Portfolio Value-at-Risk with Heavy-Tailed Risk Factors

MATHEMATICAL FINANCE, Issue 3 2002
Paul Glasserman
This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit a quadratic approximation to the portfolio loss, such as the delta-gamma approximation. In the first method, we derive the characteristic function of the quadratic approximation and then use numerical transform inversion to approximate the portfolio loss distribution. Because the quadratic approximation may not always yield accurate VAR estimates, we also develop a low variance Monte Carlo method. This method uses the quadratic approximation to guide the selection of an effective importance sampling distribution that samples risk factors so that large losses occur more often. Variance is further reduced by combining the importance sampling with stratified sampling. Numerical results on a variety of test portfolios indicate that large variance reductions are typically obtained. Both methods developed in this paper overcome difficulties associated with VAR calculation with heavy-tailed risk factors. The Monte Carlo method also extends to the problem of estimating the conditional excess, sometimes known as the conditional VAR. [source]

Unanticipated impacts of spatial variance of biodiversity on plant productivity

ECOLOGY LETTERS, Issue 8 2005
Lisandro Benedetti-Cecchi
Abstract Experiments on biodiversity have shown that productivity is often a decelerating monotonic function of biodiversity. A property of nonlinear functions, known as Jensen's inequality, predicts negative effects of the variance of predictor variables on the mean of response variables. One implication of this relationship is that an increase in spatial variability of biodiversity can cause dramatic decreases in the mean productivity of the system. Here I quantify these effects by conducting a meta-analysis of experimental data on biodiversity,productivity relationships in grasslands and using the empirically derived estimates of parameters to simulate various scenarios of levels of spatial variance and mean values of biodiversity. Jensen's inequality was estimated independently using Monte Carlo simulations and quadratic approximations. The median values of Jensen's inequality estimated with the first method ranged from 3.2 to 26.7%, whilst values obtained with the second method ranged from 5.0 to 45.0%. Meta-analyses conducted separately for each combination of simulated values of mean and spatial variance of biodiversity indicated that effect sizes were significantly larger than zero in all cases. Because patterns of biodiversity are becoming increasingly variable under intense anthropogenic pressure, the impact of loss of biodiversity on productivity may be larger than current estimates indicate. [source]