A note on Shiuʹs immunization results

The immunization problem of a portfolio with multiple liabilities is considered with respect to a wide class of interest rate shift functions depending on time. A well-known immunization theorem of Shiu on the decomposition of asset inflows is extended to this general case. Moreover generalizations of the Fong-Vasiček classical bound on the change in the value of a portfolio as well as conditions for portfolio immunization are supplied.