Assets/liabilities portfolio immunization as an optimization problem

The aim of this paper is to present bond portfolio immunization strategies in the case of multiple liabilities, based on single-risk or multiple-risk measure models under the assumption of multiple shocks in the term structure of interest rates referring, in particular, to Fong and Vasicek (1984), Nawalkha and Chambers (1996), Balbas and Ibanez (1998) and Hurlimann (2002). Immunization problem is formulated as a constrained optimization problem under a fixed open loop strategy. New risk measures associated with changes of the term structure are also defined

Extension of integrable equations

In this communication, we show that there is general construction to produce non-evolutionary integrable equations from a given integrable evolutionary equation. To support the main theorem, a few examples are explicitly given