The objective of this research is the maximization of the utility function subject to lifetime budget constraints such as personal income and consumption in each period, investments in assets, need to save for retirement, characterized by different interest rates, and discount factors. For instance, an individual may want to maximize the utility obtained by spending money on food, rent, sports, hobbies, and investments with a given monthly salary.

Due to the uncertain nature of future income and investment returns, a robust optimization approach is used to deal with the life-cycle consumption problem to find solutions that perform well even in adverse conditions. However, this problem can be hard to solve when long horizons and different assumptions related to the degree of uncertainty of the future are considered.

Thanks to Artelys Knitro and the methodology proposed by the authors, instances with a time horizon of 30 years can be solved efficiently, and solutions that deliver the highest utility for worst-case scenarios of future returns can be identified.