John Sang Jin Kang from University of Western Ontario.
Paper: Moment-Based Density Approximation Methodologies with Actuarial Applications
Several advances in connection with certain aspects of distribution theory and its applications are proposed. First, we focus on heavy-tailed distributions, such as the Pareto, Student-t and Cauchy, which only possess a finite number of moments, if any. We suggest applying the Esscher transform to such distributions, which then enables one to make use of an accurate moment-based density approximation methodology. This involves solving systems of equations that are explicitly provided for the univariate and bivariate cases. A symmetrization technique is also proposed to address instances wherein the methodology can only be applied to truncated distributions that are defined on the positive half-line. As well, we are introducing a novel technique ensuring that the polynomial adjustments being made to appropriately selected base density functions remain positive and differentiable so that the resulting functions be bona fide densities. It is also explained that one can utilize the proposed approach in the context of density estimation, in which case sample moment are employed in lieu of exacts moments. Several illustrative examples involving actuarial data sets will be presented.