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A straightforward analytical calculation of the distribution of an annuity certain with stochastic interest rate. (English) Zbl 0893.62105

Summary: Starting from the moment generating function of the annuity certain with stochastic interest rate written by means of a time discretization of the Wiener process as an \(n\)-fold integral, a straightforward evaluation of the corresponding distribution function is obtained by letting \(n\) tend to infinity. The advantage of the present method consists in the direct calculation technique of the \(n\)-fold integral, instead of using moment calculation or differential equations, and in the possible applicability of the present method to varying annuities which could be applied to IBNR results, as well as to pension fund calculations, etc.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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