B1531
Title: Computing the distribution of collective risk models via numerical inversion the characteristic function
Authors: Gejza Wimmer - Mathematical Institute, Slovak Academy of Sciences (Slovakia) [presenting]
Viktor Witkovsky - Slovak Academy of Sciences (Slovakia)
Abstract: A typical model for insurance risk is the collective risk model (CRM). The collective risk model mathematically describes the aggregate loss of an insurance portfolio in a certain period of time (e.g. 1 year). Insurance portfolio is regarded as a process that produces claims over time. The sizes of these claims are taken to be independent, identically distributed random variables independent also of the number of claims generated in this time period. We present the typical parametric collective risk models and their characteristic functions (CFs), and introduce a new MATLAB Toolbox called CRM for high precision calculation of probability density functions (PDF) and cumulative distribution functions (CDF) of the CRM distributions. Method of calculation is based on the numerical inversion of CRM's characteristic function. The suggested numerical approaches are based on the Gil-Pelaez inversion formulae for computing the probability distribution functions (PDF and/or CDF) of the univariate continuous random variables. Moreover, a non-parametric method based on inverting the empirical characteristic functions is presented and illustrated.
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