A combined stochastic programming and optimal control approach to personal finance and pensions

We combine a dynamic programming approach (stochastic optimal control) with a multi-stage stochastic programming approach (MSP) in order to solve various problems in personal finance and pensions. Both optimization methods are integrated into one MSP formulation, making it possible to achieve a solution within a short computational time. The solution takes into account the entire lifetime of an individual, while focusing on practical constraints, such as limits on portfolio composition, limits on the sum insured, inclusion of transaction costs, and taxes on capital gains, during the first years of a contract. Two applications are considered: (A) optimal investment, consumption and sum insured for an individual maximizing the expected utility of consumption and bequest, and (B) optimal investment for a pension saver who wishes to maximize the expected utility of retirement benefits. Numerical results show that among the considered practical constraints, the presence of taxes affects the optimal controls the most. Furthermore, the individual’s preferences, such as impatience level and risk aversion, have even a higher impact on the controlled processes than the taxes on capital gains.