A stochastic model for financial evaluation: Applications to actuarial constructs (Q2711695)

In the recent actuarial literature, the problem of the evaluation of actuarial functions is often considered in a stochastic interest environment. In fact, the total riskiness for the insurers consists of the well-known adverse deviations of a strictly ``actuarial nature'' and of some stochastic components, essentially connected to investment risk. Both these elements and their interaction determine adverse deviations from expectations. NEWLINENEWLINENEWLINEMany stochastic financial models have been treated to describe interest randomness in evaluating actuarial functions: description of the investment performance deviations over time in collective risk theory; presentation of a stochastic capitalization model for financial risk in actuarial business; evaluation of life annuities under the hypotheses of stochastic mortality and interest; consideration of a stochastic force of ~interest in evaluating the present value of benefits for a portfolio of identical policies and a portfolio of identical endowment insurance contracts; modelling the force of interest by a homogeneous time-continuous Markov chain with finite space; and consideration of applications in insurance. The first two of the authors of this paper have recently presented a stochastic process for the force of interest and a model for the net instantaneous inflation rate. This paper presents a model for the force of interest which is based on the consideration of a real force of interest deviations from its estimated value; the resulting stochastic process for financial evaluation is characterized by its expected value and autocovariance functions. Namely, it is considered that the force of interest \(Y_{t}\) is the sum of a deterministic component \(\delta_{t}\) and a stochastic one \(X_{t}\) that describe the deviations of time: \(Y_{t}=\delta_{t}+X_{t}.\) It is supposed that the stochastic component \(X_{t}\) follows an Ornstein-Uhlenbeck process. Applications of the results to actuarial contracts are proposed. In particular, the cases of temporary life annuity and \(n\)-year termlife insurance are considered and their expected values and variances are illustrated.