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Two Stochastic Approaches for Discounting Actuarial Functions
 Proceedings of the XXIV ASTIN Colloquium
, 1993
"... Two approaches used to model interest randomness are presented. They are the modeling of the force of interest accumulation function and the modeling of the force of interest. The expected value, standard eviation and coefficient of skewness of the present value of annuitiesimmediate are presented ..."
Abstract

Cited by 13 (0 self)
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Two approaches used to model interest randomness are presented. They are the modeling of the force of interest accumulation function and the modeling of the force of interest. The expected value, standard eviation and coefficient of skewness of the present value of annuitiesimmediate are presented as illustrations. The implicit behavior of the force of interest under the two approaches i investigated by looking at a particular conditional expectation of the force of interest accumulation function.
LONGTERM RETURNS IN STOCHASTIC INTEREST RATE MODELS: APPLICATIONS B¥
"... We extend the CoxIngersollRoss (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have s ..."
Abstract

Cited by 9 (3 self)
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We extend the CoxIngersollRoss (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the longterm return by using the theory of generalised Besselsquare processes. We emphasize the applications of the convergence results. A limit theorem proves evidence of the use of a Brownian motion with drift instead of the integral fg rudu. For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very timeconsuming.