Søren Asmussen, Pierre-Olivier Goffard, Patrick J. Laub
Approximations for an unknown density g in terms of a reference density fν and its associated orthonormal polynomials are discussed. The main application is the approximation of the density f of a sum S of lognormals which may have different variances or be dependent. In this setting, g may be f itself or a transformed density, in particular that of log S or an exponentially tilted density. Choices of reference densities fν that are considered include normal, gamma and lognormal densities. For the lognormal c…
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