A COUNTING PROCESS APPROACH TO STOCHASTIC INTEREST

The aim of the present paper is to propose a stochastic approach for d escribing the return of an investment, and study its applications in i nsurance. The process governing the return of the investment is assume d to have bounded variation over finite intervals and possess a jump p art. Attention is restricted to cases where the process has independen t increments and is subject to fluctuations given by a Markovian envir onment. In the first case direct calculations are obtainable for evalu ating moments of present and accumulated values. In the last case we e stablish differential equations akin to the celebrated Thiele's differ ential equation in life insurance.