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A maximum principle for relaxed stochastic control of linear SDEs with application to bond portfolio optimization

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  • Daniel Andersson
  • Boualem Djehiche

Abstract

We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and necessary conditions for optimality in the form of a relaxed maximum principle. The main motivation is an optimal bond portfolio problem in a market where there exists a continuum of bonds and the portfolio weights are modeled as measure-valued processes on the set of times to maturity. Copyright Springer-Verlag 2010

Suggested Citation

  • Daniel Andersson & Boualem Djehiche, 2010. "A maximum principle for relaxed stochastic control of linear SDEs with application to bond portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 273-310, October.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:2:p:273-310
    DOI: 10.1007/s00186-010-0320-7
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    References listed on IDEAS

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    1. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    2. Seïd Bahlali & Brahim Mezerdi & Boualem Djehiche, 2006. "Approximation and optimality necessary conditions in relaxed stochastic control problems," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-23, June.
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    Cited by:

    1. Daniel Andersson, 2008. "A mixed relaxed singular maximum principle for linear SDEs with random coefficients," Papers 0812.0136, arXiv.org, revised Dec 2008.

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