RISK THEORY: EXACT CALCULATIONS IN THE INDIVIDUAL RISK MODEL; SOME METHODS

The Authors state that in the paper they will only analyse exact calculations of the individual model, without any prefixed distribution; in other words, the paper is aimed at studying the individual risk theory considering an insurance policy (of an insurance portfolio or of a pension fund) as a random variable that describes the possible events and the yearly cash flow during a fixed period of time (not in general longer than twenty years). The sum of this random gives the cash flow probability distribution -evaluated either in case of deterministic or in case of stochastic rate of interest- for the whole portfolio (or for the whole pension fund) without any limitation except for the hypothesis that the random variable realizations are integer and finite numbers. The first part of the paper shows the basic exact method based on the characteristic function of discrete and mutually independent random variables but not having necessarily the same distribution (integer realizations). One of the most useful mathematical tools used for the demonstrations of is the exact Inverse Discrete Fourier Transform. The second part of the paper shows applications about pension funds.