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A dynamic programming approach to constrained portfolios

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  • Kraft, Holger
  • Steffensen, Mogens

Abstract

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter-mediate wealth and/or consumption.

Suggested Citation

  • Kraft, Holger & Steffensen, Mogens, 2012. "A dynamic programming approach to constrained portfolios," CFS Working Paper Series 2012/07, Center for Financial Studies (CFS).
  • Handle: RePEc:zbw:cfswop:201207
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    References listed on IDEAS

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    More about this item

    Keywords

    Finance; Markov Processes; Consumption-investment Problems; Utility Maximization; Bellman Equations;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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