Extension of Khang's Immunization Formula

摘要

The paper presents two theorems on immunization in the continuous context when a liability consists of a single outflow at a known future date. It is assumed in Theorem 1 that interest rates h(0,t) shift to their new values h(0,t) = h(0,t) = h(0,t) + f(#lambda#)a(t) where #lambda# is a continuous function and f(#lambda#) is twice continuously differentiable with f(0) = 0, f'(0) not= 0. It is proved that the local immunization is achieved and a formula for the immunizing duration is derived. Theorem 2 provides a formula for the immunizing duration of the portfolio combined with two cash flows. These two theorems extend validity of all similar type results presented by Bierwag (1983).