Robust Solutions to the Life-Cycle Consumption Problem.

Abstract

This paper demonstrates how the well-known discrete life-cycle consumption prob_x005F_x0002_lem (LCP) can be solved using the Robust Counterpart (RC) formulation technique, as defined in Ben-Tal and Nemirovski (Math Oper Res 23(4):769–805, 1998). To do this, we propose a methodology that involves applying a change of variables over the original consumption before deriving the RC. These transformations allow deriving a closed solution to the inner problem, and thus to solve the LCP without facing the curse of dimensionality and without needing to specify the prior distribution for the invest_x005F_x0002_ment opportunity set. We generalize the methodology and illustrate how it can be used to solve other type of problems. The results show that our methodology enables solv_x005F_x0002_ing long-term instances of the LCP (30 years). We also show it provides an alternative consumption pattern as to the one provided by a benchmark that uses a dynamic pro_x005F_x0002_gramming approach. Rather than finding a consumption that maximizes the expected lifetime utility, our solution delivers higher utilities for worst-case scenarios of future returns