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A theory of bond portfolios

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  • Ivar Ekeland
  • Erik Taflin
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    Abstract

    We introduce a bond portfolio management theory based on foundations similar to those of stock portfolio management. A general continuous-time zero-coupon market is considered. The problem of optimal portfolios of zero-coupon bonds is solved for general utility functions, under a condition of no-arbitrage in the zero-coupon market. A mutual fund theorem is proved, in the case of deterministic volatilities. Explicit expressions are given for the optimal solutions for several utility functions.

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    File URL: http://arxiv.org/pdf/math/0301278
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number math/0301278.

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    Date of creation: Jan 2003
    Date of revision: May 2005
    Publication status: Published in Annals of Applied Probability 2005, Vol. 15, No. 2, 1260-1305
    Handle: RePEc:arx:papers:math/0301278

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    Web page: http://arxiv.org/

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    References

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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.
    2. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
    3. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    4. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
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    Cited by:
    1. Erik Taflin, 2009. "Generalized integrands and bond portfolios: Pitfalls and counter examples," Papers 0909.2341, arXiv.org, revised Jan 2011.
    2. Bruno Bouchard & Emmanuel Lepinette & Erik Taflin, 2013. "Robust no-free lunch with vanishing risk, a continuum of assets and proportional transaction costs," Papers 1302.0361, arXiv.org.
    3. Fred Espen Benth & Paul Kr\"uhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    4. Andersson, Patrik & Lagerås, Andreas N., 2013. "Optimal bond portfolios with fixed time to maturity," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 429-438.
    5. Oleksii Mostovyi, 2014. "Utility maximization in the large markets," Papers 1403.6175, arXiv.org.
    6. Irene Klein & Thorsten Schmidt & Josef Teichmann, 2013. "When roll-overs do not qualify as num\'eraire: bond markets beyond short rate paradigms," Papers 1310.0032, arXiv.org.
    7. Fred Espen Benth & Jukka Lempa, 2012. "Optimal portfolios in commodity futures markets," Papers 1204.2667, arXiv.org.
    8. Yal\c{c}in Aktar & Erik Taflin, 2014. "A remark on smooth solutions to a stochastic control problem with a power terminal cost function and stochastic volatilities," Papers 1405.3566, arXiv.org.

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