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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 85, 2013 - Issue 4: Taksar Memorial Issue
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Original Articles

Deterministic mean-variance-optimal consumption and investment

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Pages 620-636 | Received 27 Feb 2013, Accepted 30 Apr 2013, Published online: 18 Jun 2013
 

Abstract

In dynamic optimal consumption–investment problems one typically aims to find an optimal control from the set of adapted processes. This is also the natural starting point in case of a mean-variance objective. In contrast, we solve the optimization problem with the special feature that the consumption rate and the investment proportion are constrained to be deterministic processes. As a result we get rid of a series of unwanted features of the stochastic solution including diffusive consumption, satisfaction points and consistency problems. Deterministic strategies typically appear in unit-linked life insurance contracts, where the life-cycle investment strategy is age dependent but wealth independent. We explain how optimal deterministic strategies can be found numerically and present an example from life insurance where we compare the optimal solution with suboptimal deterministic strategies derived from the stochastic solution.

2000 Mathematics Subject Classification::

Notes

Additional information

Notes on contributors

Mogens Steffensen

1 1 [email protected]

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