A Combined Stochastic Programming and Optimal Control Approach to Personal Finance and Pensions

37 Pages Posted: 6 May 2014 Last revised: 26 Jun 2015

See all articles by Agnieszka K. Konicz Bell

Agnieszka K. Konicz Bell

Independent

David Pisinger

Technical University of Denmark - Management Engineering

Kourosh Marjani Rasmussen

Technical University of Denmark

Mogens Steffensen

University of Copenhagen

Date Written: April 30, 2014

Abstract

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. Stochastic optimal control produces an optimal policy that is easy to understand and implement. However, explicit solution may not exist, especially when we want to deal with constraints, such as limits on portfolio composition, limits on the sum insured, an inclusion of transaction costs or taxes on capital gains, which are important issues regularly mentioned in the literature. Both optimization methods are integrated into one MSP formulation, and in a short computational time produce a solution, which takes into account the entire lifetime of an individual with a focus on the practical constraints 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.

Keywords: dynamic programming, multi-period stochastic programming, power utility, personal finance, retirement

JEL Classification: C44, C61, G11, G22, G23

Suggested Citation

Konicz Bell, Agnieszka K. and Pisinger, David and Rasmussen, Kourosh Marjani and Steffensen, Mogens, A Combined Stochastic Programming and Optimal Control Approach to Personal Finance and Pensions (April 30, 2014). 2015, OR Spectrum: 37(3):583-616. Available at SSRN: https://ssrn.com/abstract=2432869 or http://dx.doi.org/10.2139/ssrn.2432869

Agnieszka K. Konicz Bell (Contact Author)

Independent ( email )

No Address Available

David Pisinger

Technical University of Denmark - Management Engineering ( email )

Produktionstorvet 424
room 043
Kgs. Lyngby, 2800
Denmark

Kourosh Marjani Rasmussen

Technical University of Denmark ( email )

Anker Engelunds Vej 1
Building 101A
Lyngby, 2800
Denmark

Mogens Steffensen

University of Copenhagen ( email )

Universitetsparken 5
DK-2100 Copenhagen
Denmark

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