  We consider the problem of seeking an optimal set of model points associated
to a fixed portfolio of life insurance policies. Such an optimal set is
characterized by minimizing a certain risk functional, which gauges the average
discrepancy with the fixed portfolio in terms of the fluctuation of the
interest rate term structure within a given time horizon. We prove a
representation theorem which provides two alternative formulations of the risk
functional and which may be understood in connection with the standard
approaches for the portfolio immunization based on sensitivity analysis. For
this purpose, a general framework concerning some techniques of stochastic
integration in Banach space and Malliavin calculus is introduced. A numerical
example is discussed when considering a portfolio of whole life policies.
