Fair evaluation of life insurance policies with periodic rebalancing between asset portfolios and interest rate guarantee

We consider the problem of evaluating at fair rates an innovative life insurance policy with a rebalancing scheme between different asset portfolios and an embedded interest rate guarantee. The premiums are invested in two portfolios of assets characterized by different levels of risk and sums are transferred from one fund to the other at some prefixed dates, depending on the performance of the funds. The dynamics of each fund is approximated by means of binomial lattices but, since the remixing feature makes the evolution of the riskier fund path- dependent, we propose a model based on "representative" values to keep the computational cost of the evaluation problem at a reasonable level. The usual backward induction coupled with linear interpolation allows us to determine the policy value at inception.