Optimal portfolio allocation under asset and surplus VaR constraints

In this paper, we propose an approach to asset liability management of various institutions, in particular in insurance companies, based on a dual value at risk (VaR) constraint for the asset and the surplus. A key ingredient of this approach is a flexible modelling of the term structure of interest rates leading to an explicit formula for the returns of bonds. VaR constraints on the asset and on the surplus also take tractable forms, and graphical illustrations of the impact and of the sensitivity of these constraints are easily explicited in terms of various parameters: share of stocks, duration and convexity of the bonds on the asset and liability sides, expected return and volatility of the asset.