Description: In this paper, the relationship of convexity to the assumption of parallel shifts is explored, and new convexity measures are developed to reflect nonparallel shifts. These new measures can differ dramatically from the traditional values, providing insight into when convexity does not have to be good and when it does.

Description: In this paper, a general multivariate duration analysis is introduced that does not depend on a mathematical formulation of the way in which a yield curve moves. A discussion of the paper follows. From Transactions of Society of Actuaries 1991, Vol. 43.

Description: With this paper, a new theory of immunization is introduced in which the approach is multivariate, and the goal is stochastic in the sense of minimizing stochastic risk. Discussions of this paper are included.

Description: This paper discusses extending the general nonparallel shift approach to duration analysis developed previously and explores the immunization model within the multivariate context. A discussion of the paper follows. From Transactions of Society of Actuaries 1991, Vol. 43.