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A theory of bond portfolios

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  • Ivar Ekeland
  • Erik Taflin

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.

Suggested Citation

  • Ivar Ekeland & Erik Taflin, 2003. "A theory of bond portfolios," Papers math/0301278, arXiv.org, revised May 2005.
    • Handle: RePEc:arx:papers:math/0301278
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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. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. 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 247-257, August.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    5. Erik Taflin, 2002. "Equity Allocation And Portfolio Selection In Insurance: A Simplified Portfolio Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 223-253.
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    Citations

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    Cited by:

    1. 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.
    2. Jacek Jakubowski & Jerzy Zabczyk, 2007. "Exponential moments for HJM models with jumps," Finance and Stochastics, Springer, vol. 11(3), pages 429-445, July.
    3. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    4. Charles Shaw, 2022. "Portfolio Diversification Revisited," Papers 2204.13398, arXiv.org.
    5. Nathanael Ringer & Michael Tehranchi, 2006. "Optimal portfolio choice in the bond market," Finance and Stochastics, Springer, vol. 10(4), pages 553-573, December.
    6. Fred Benth & Jukka Lempa, 2014. "Optimal portfolios in commodity futures markets," Finance and Stochastics, Springer, vol. 18(2), pages 407-430, April.
    7. Erik Taflin, 2009. "Generalized integrands and bond portfolios: Pitfalls and counter examples," Papers 0909.2341, arXiv.org, revised Jan 2011.
    8. 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.
    9. Enrico Ferri, 2018. "Infinite dimensional portfolio representation as applied to model points selection in life insurance," Papers 1808.00866, arXiv.org, revised Mar 2020.
    10. 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.
    11. Oleksii Mostovyi, 2014. "Utility maximization in the large markets," Papers 1403.6175, arXiv.org, revised Oct 2014.
    12. Yalc{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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