Stochastic Models for Optimizing Immunization Strategies in Fixed-Income Security Portfolios under Some Sources of Uncertainty

In this paper we present a set of approaches for stochastic optimizing of immunization strategies based on risk averse measures as alternatives to the optimization of the objective function expected value, i.e., in the so-called risk neutral environment. The risk averse measures to consider whose validity is analyzed in this work are as follows: two-stage mean-risk immunization, two-stage and multistage Value-at-Risk strategy, two-stage and multistage stochastic dominance strategy, and a new measure as a mixture of the multistage VaR & stochastic dominance strategies. The common characteristic of these measures is that they require from the modeler a threshold for the objective function value related to each scenario (the recent ones even allow a set of thresholds) and a failure probability when not reaching it. Uncertainty is represented by a scenario tree and is dealt with by both two-stage and multi-stage stochastic (linear and) mixed integer models with complete recourse. We will test the different risk averse strategies presented in the paper by using, as a pilot case, the optimization of the immunization strategies in fixed-income security portfolios under some sources of uncertainty. One of the main differences in the bond portfolio strategies that are proposed in the work and the models that have been encountered in the literature is that we consider an investor who wishes to invest in a market with coupon bonds that have a different level of risk of default.