On probability distributions of present values in life insurance
Section 2 deals briefly with models involving only a finite number of random variables. In such situations the distributions of present values (and any other functions of the random variables) can be obtained by integrating the finite-dimensional distribution. This approach comes down overagainst more complex situations where stochastic processes have to be employed. In Section 3 we consider a general multistate insurance policy with payments of assurance and annuity types and with state-dependent force of interest. Assuming that the state process is Markov, we derive in Section 4 a set of integral equations for the conditional probability distribution function of the present value of future benefits less premiums, given the state at the time of consideration. The equations are converted to a differential form that constitutes the basis of a computational scheme. Examples of applications, including numerical illustrations, are given in Section 5.
scientific article; zbMATH DE number 923766