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Optimal Investment Decisions For A Portfolio With A Rolling Horizon Bond And A Discount Bond

Author

Listed:
  • TOMASZ R. BIELECKI

    (Applied Mathematics Department, Illinois Institute of Technology, Chicago IL 60616, USA)

  • STANLEY PLISKA

    (Department of Finance, University of Illinois at Chicago, Chicago IL 60607-7124, USA)

  • JIONGMIN YONG

    (Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics, and Institute of Mathematical Finance, Fudan University, Shanghai 200433, China)

Abstract

An optimal investment problem is considered for a continuous-time market consisting of the usual bank account, a rolling horizon bond, and a discount bond whose maturity coincides with the planning horizon. Two economic factors, namely, the short rate and the risk-free yield of some fixed maturity, are modeled as Gaussian processes. For the problem of maximizing expected CRRA utility of terminal wealth, the optimal portfolio is obtained through a Bellman equation. The results are noteworthy because the discount bond, which is the riskless asset for the investor, causes a degeneracy due to its zero volatility at the planning horizon. Indeed, this delicate matter is treated rigorously for what seems to be the first time, and it is shown that there exists an optimal, admissible (but unbounded) trading strategy.

Suggested Citation

  • Tomasz R. Bielecki & Stanley Pliska & Jiongmin Yong, 2005. "Optimal Investment Decisions For A Portfolio With A Rolling Horizon Bond And A Discount Bond," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(07), pages 871-913.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:07:n:s0219024905003335
    DOI: 10.1142/S0219024905003335
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    Citations

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    Cited by:

    1. Eckert, Johanna & Gatzert, Nadine & Martin, Michael, 2016. "Valuation and risk assessment of participating life insurance in the presence of credit risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 382-393.
    2. Jakub Trybu{l}a & Dariusz Zawisza, 2014. "Continuous time portfolio choice under monotone preferences with quadratic penalty - stochastic interest rate case," Papers 1404.5408, arXiv.org.
    3. Syarifuddin, Ferry, 2020. "An Optimal Islamic Investment Decision in Two-region Economy: The Case of Indonesia and Malaysia," MPRA Paper 104809, University Library of Munich, Germany.
    4. Ankush Agarwal & Christian-Oliver Ewald & Yongjie Wang, 2023. "Hedging longevity risk in defined contribution pension schemes," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    5. Szymon Peszat & Dariusz Zawisza, 2020. "The investor problem based on the HJM model," Papers 2010.13915, arXiv.org, revised Dec 2021.

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