Optimal portfolio selection for general provisioning and terminal wealth problems

In Dhaene et al. (2005), multiperiod portfolio selection problems are discussed,
using an analytical approach to find optimal constant mix investment strategies in
a provisioning or savings context. In this paper we extend some of these results,
investigating some specific, real-life situations. The problems that we consider in
the …rst section of this paper are general in the sense that they allow for liabilities
that can be both positive or negative, as opposed to Dhaene et al. (2005), where
all liabilities have to be of the same sign. Secondly, we generalize portfolio selection
problems to the case where a minimal return requirement is imposed. We derive an
intuitive formula that can be used in provisioning and terminal wealth problems as a
constraint on the admissable investment portfolios, in order to guarantee a minimal
annualized return. We always apply our results to optimal portfolio selection.