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01-07-2015 | Regular Article

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

Authors: Agnieszka Karolina Konicz, David Pisinger, Kourosh Marjani Rasmussen, Mogens Steffensen

Published in: OR Spectrum | Issue 3/2015

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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. 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.

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A similar approach to life insurance contracts can be found in Kraft and Steffensen (2008). The assumption about tradability of life insurance is not substantially different from considering a case where policy holders are allowed to make alterations to their contracts. Apart from realistic issues with health and other types of assymetric information (which do not appear in our model), this is certainly what appears in practice.

The model could be extended by adding a stochastic labor income. However, the explicit solutions to problems (A) and (B) can be derived only if the labor income is assumed to be spanned by the stock risk. Otherwise, explicit solutions to the control problems do not exist.

In principle, the mortality intensity model does not assume that an individual is dead at time \(\widetilde{T}\) with probability 1. However, for \(\widetilde{T}=110\), this error is negligible.

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Title: A combined stochastic programming and optimal control approach to personal finance and pensions
Authors: Agnieszka Karolina Konicz
David Pisinger
Kourosh Marjani Rasmussen
Mogens Steffensen
Publication date: 01-07-2015
Publisher: Springer Berlin Heidelberg
Published in: OR Spectrum / Issue 3/2015
Print ISSN: 0171-6468
Electronic ISSN: 1436-6304
DOI: https://doi.org/10.1007/s00291-014-0375-6

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