Convolution and Actuarial Risk in a Pension Fund

Note Description

The aim of the paper is to propose a new method to evaluate the actuarial risks in a pension fund. We recall: a) the utilisation of discrete Fourier transforms in the random variables (with integer realisations) to calculate convolutions in an exact and fast way. [par 1A]; b) the contributions and benefits definition according to the" Projected Unit Method" Guidance Note 9;[par. 1B]. The idea is to apply the distribution of the sum of the random variables to calculate the risk directly. That is done by multiplying each probability (of a sum of random variables) for the corresponding negative realisation (each realisation of any employee, for each year, is the difference between the accrued contributions and the corresponding benefits). The first application is the calculus of guarantee in a defined benefit pension fund, particularly the guarantee that -every year- the the succession of assets is not minor than the succession of liabilities

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