308 citations · 322 across the 8 of their papers we have counts for
8 papers
Quantile Mechanics 3: Series Representations and Approximation of some Quantile Functions appearing in Finance
Asad Munir, William Shaw
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for…
Complex Variable Methods for 3D Applied Mathematics: 3D Twistors and the biharmonic equation
William T. Shaw
In applied mathematics generally and fluid dynamics in particular, the role of complex variable methods is normally confined to two-dimensional motion and the association of points…
Monte Carlo sampling given a Characteristic Function: Quantile Mechanics in Momentum Space
William T. Shaw, Jonathan McCabe
In mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density funct…
The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map
William T. Shaw, Ian R. C. Buckley
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering w…
A simple resolution of Stokes' paradox?
William T. Shaw
This paper proposes a solution to Stokes' paradox for asymptotically uniform viscous flow around a cylinder. The existence of a {\it global} stream function satisfying a perturbati…
Quantile Mechanics II: Changes of Variables in Monte Carlo methods and GPU-Optimized Normal Quantiles
William T. Shaw, Thomas Luu, Nick Brickman
This article presents differential equations and solution methods for the functions of the form , where and are cumulative distribution functions. Such…