Στοχαστικά μοντέλα για ράντες πληρωμών
Recursive relationships for annuities models under random rates of interest
Καραμπέτσος, Αλέξανδρος Κ.
In this paper we will study stochastic models for annuities due to random rate of interest. We will consider a stochastic approach to the theory of interest taking into account that the rate of interest i is a random variable. We will also study the accumulated values of certain annuities for a specific period of time, and we will calculate their expected values and variances. For this aim we suggest two methods, one of which, from the mathematical point of view is preferable in terms of the simplicity of calculations, due to the recursive relations used. Further, we will introduce the basic theory of stochastic processes and in particular, the Brownian motion and its special cases. Finally, we will present two stochastic methods for the modeling of the "randomness" of the interest rate, as well as numerical results will be presented.