Abstract
In the current 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. The risk measure utilized is reminiscent of the Markowitz [4] approach of variance minimization but generalized to also reflect a measure of worst-case risk. The approach is multivariate in that full yield curve risk to nonparallel shifts is reflected, as Reitano [6-13], by modeling the yield curve as a vector of yield curve drivers. Explicit solutions to the risk minimization problems are developed, subject to constraints on portfolio returns and/or various portfolio directional durations. In addition, explicit solutions are determined that can be achieved by trading any given collection of assets. Applications are developed in detail and are exemplified by an analysis of the example introduced in Reitano [11].