In this work, we pose and solve a mean square optimal hedging problem that takes higher order moments (or cumulants) into account. We first provide a discrete stochastic dynamics model using a general multinomial lattice, where the first m cumulants are matched over each time step. We then analyze the effect of higher order moments in the underlying asset process on the price of derivative secu...

Time-integrated fluorescence cumulant analysis (TIFCA) is a data analysis technique for fluorescence fluctuation spectroscopy (FFS) that extracts information from the cumulants of the integrated fluorescence intensity. It is the first exact theory that describes the effect of sampling time on FFS experiment. Rebinning of data to longer sampling times helps to increase the signal/noise ratio of ...

Negative binomial and Poisson processes {X(t), t ≥ 0} have cumulants proportional to the rate λ. So, formal Cornish-Fisher expansions in powers of λ−1/2 are available for their cumulative distribution function and quantiles. If T is an independent random variable with cumulants proportional to γ then the cumulants of X(T ) are proportional to γ; so, CornishFisher expansions in powers of γ−1/2 a...

Recursive and least squares methods for identification of non-minimum-phase linear time-invariant (NMP-LTI) FIR systems are developed. The methods utilize the secondand third-order cumulants of the output of the FIR system whose input is an independent, identically distributed (i.i.d.) non-Gaussian process. Since knowledge of the system order is of utmost importance to many system identificatio...

From a finite-size scaling (FSS) theory of cumulants of the order parameter at phase coexistence points, we reconstruct the scaling of the moments. Assuming that the cumulants allow a reconstruction of the free energy density no better than as an asymptotic expansion, we find that FSS for moments of low order is still complete. We suggest ways of using this theory for the analysis of numerical ...

Cumulants are useful in studying nonlinear phenomena and in developing (approximate) statistical properties of quantities computed from random process data. Wavelet analysis is a powerful tool for the approximation and estimation of curves and surfaces. This work considers both wavelets and cumulants, developing some sampling properties of linear wavelet fits to a signal in the presence of addi...

Fixation indices summarize the associations between genes that arise from the joint effects of inbreeding and selection. In this paper, fixation indices are derived for pairs, triplets and quadruplets of genes at a single multiallelic locus. The fixation indices are obtained by dividing cumulants by constants; the cumulants describe the statistical distribution of alleles and the constants are ...

We propose a novel algebraic algorithmic framework for dealing with probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by tr...