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A theory of bond portfolios

Author

Listed:
  • 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

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