Infinite dimensional portfolio representation as applied to model points selection in life insurance

TL;DR

This paper develops an infinite-dimensional framework for selecting optimal model points in life insurance portfolios by minimizing a risk functional related to interest rate fluctuations, using advanced stochastic calculus techniques.

Contribution

It introduces a novel infinite-dimensional representation of the risk functional and connects it with standard immunization approaches through stochastic integration and Malliavin calculus.

Findings

Representation theorem for the risk functional

Alternative formulations linked to portfolio immunization

Numerical example with whole life policies

Abstract

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.