The state price density of a basket, even under uncorrelated Black–Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in Financial and Actuarial Mathematics.) In this note we discuss short time and small volatility expansions, respectively. The method works for gene...

My original query some time ago – one computer crash ago was about the amplitude probability density function (pdf) of surface EMG data (from which we have subtracted the mean value). That is, if one plots the amplitude of the rectified EMG in an histogram, what does it look like? The common assumption is that we get a (one-sided) Gaussian pdf for stationary data. This is generally so. However,...

A continuous case of new density function called harmonic probability density function (HPDF) is structured using mathematical method. The mean and variance of this probability function is presented using both the definition and moment generating function. A discussion has started on many other connections that may exist between this new model and its applications in geometry, probability, and ...