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 innovativelife insurance policy with a rebalancing scheme between different as-set portfolios and an embedded interest rate guarantee. The premiumsare invested in two portfolios of assets characterized by different levelsof risk and sums are transferred from one fund to the other at someprefixed dates, depending on the performance of the funds. The dy-namics 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 keepthe computational cost of the evaluation problem at a reasonable level.The usual backward induction coupled with linear interpolation allowsus to determine the policy value at inception.