Abstract
An individual investor has to decide how to allocate his/her savings from a retirement perspective. This problem covers a long-term horizon.
In this paper we consider a 40-year horizon formulating a multi-criteria multistage program with stochastic dominance constraints in an intermediate stage and in the final stage. As we are dealing with a real problem and we have formulated the model in cooperation with a commercial Italian bank, the intermediate stage corresponds to a possible withdrawal allowed by the Italian pension system.
The sources of uncertainty considered are: the financial returns, the interest rate evolution, the investor's salary process and a considerable withdrawal event. We include a set of portfolio constraints according to the pension plan regulation.
The objective of the model is to minimize the Average Value at Risk Deviation measure and to satisfy wealth goals. Three different wealth target formulations are considered: a deterministic wealth target (i.e. a comparison between the accumulated average wealth and a fixed threshold) and two stochastic dominance relations-the first order and the second order-introducing a benchmark portfolio and then requiring the optimal portfolio to dominate the benchmark.
In particular, we prove that solutions obtained under stochastic dominance constraints ensure a safer allocation while still guaranteeing good returns. Moreover, we show how the withdrawal event affects the solution in terms of allocation in each of the three frameworks.
Finally, the sensitivity and convergence of the stochastic solutions and computational issues are investigated.