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A dynamic programming approach to constrained portfolios

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  • Kraft, Holger
  • Steffensen, Mogens
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    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. --

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    Bibliographic Info

    Paper provided by Center for Financial Studies (CFS) in its series CFS Working Paper Series with number 2012/07.

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    Date of creation: 2012
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    Handle: RePEc:zbw:cfswop:201207

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

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    1. Suleyman Basak & Alex Shapiro, . "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 06-99, Wharton School Rodney L. White Center for Financial Research.
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