IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v08y2005i02ns0219024905002962.html
   My bibliography  Save this article

Optimal Investment Strategy Via Interval Arithmetic

Author

Listed:
  • BENITO STRADI

    (Department of AFM and Essex Finance Center (EFiC), University of Essex, Wivenhoe Park, Colchester C04 3SQ, UK)

  • EMMANUEL HAVEN

    (Department of AFM and Essex Finance Center (EFiC), University of Essex, Wivenhoe Park, Colchester C04 3SQ, UK)

Abstract

This paper studies the optimal replacement policy of an item that experiences stochastic geometric growth in maintenance costs. The model integrates corporate taxes, tax credits, depreciation, and salvage value. We extend this traditional application to cover the cost of replacement with the payout from two bonds. The two-bond portfolio is passively immunized. The intersections between the continuation and replacement boundaries are computed using the Interval-Newton Generalized-Bisection (IN/GB) method. We allow small fluctuations of the replacement boundary. With these fluctuations, multiple intersections of the two boundaries are determined. The IN/GB method finds all these intersections without the need for initial guesses of the problem variables. This is a major computational improvement over traditional single-root finding implementations that require multiple initial guesses and provide no guarantees of existence or uniqueness. We demonstrate that without fluctuations one would expect to find a single optimal replacement time. However with fluctuations, there are several intersections of the continuation and replacement boundaries and the bond weight fractions may change by more than 200% between intersection points. These large changes in portfolio wealth allocation highlight the fragility of the idealized solution in the realm of fluctuations in replacement costs.

Suggested Citation

  • Benito Stradi & Emmanuel Haven, 2005. "Optimal Investment Strategy Via Interval Arithmetic," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 185-206.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:02:n:s0219024905002962
    DOI: 10.1142/S0219024905002962
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024905002962
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024905002962?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stradi-Granados, Benito A. & Haven, Emmanuel, 2010. "The use of interval arithmetic in solving a non-linear rational expectation based multiperiod output-inflation process model: The case of the IN/GB method," European Journal of Operational Research, Elsevier, vol. 203(1), pages 222-229, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ben Abdallah, Skander & Lasserre, Pierre, 2016. "Asset retirement with infinitely repeated alternative replacements: Harvest age and species choice in forestry," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 144-164.
    2. Oscar Gutiérrez & Francisco Ruiz-Aliseda, 2011. "Real options with unknown-date events," Annals of Finance, Springer, vol. 7(2), pages 171-198, May.
    3. Timothy Erickson & Toni M. Whited, 2000. "Measurement Error and the Relationship between Investment and q," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 1027-1057, October.
    4. Arve, Malin & Zwart, Gijsbert, 2023. "Optimal procurement and investment in new technologies under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    5. Shively, Gerald E., 2001. "Price thresholds, price volatility, and the private costs of investment in a developing country grain market," Economic Modelling, Elsevier, vol. 18(3), pages 399-414, August.
    6. Marks, Phillipa & Marks, Brian, 2007. "Spectrum Allocation, Spectrum Commons and Public Goods: the Role of the Market," MPRA Paper 6785, University Library of Munich, Germany.
    7. Stern, Nicholas, 2018. "Public economics as if time matters: Climate change and the dynamics of policy," Journal of Public Economics, Elsevier, vol. 162(C), pages 4-17.
    8. Krause, M.U., 2002. "Inter-Industry Wage Differentials and Job Flows," Discussion Paper 2002-3, Tilburg University, Center for Economic Research.
    9. Wong, Kit Pong & Yi, Long, 2013. "Irreversibility, mean reversion, and investment timing," Economic Modelling, Elsevier, vol. 30(C), pages 770-775.
    10. Pierre‐Richard Agénor, 2004. "Macroeconomic Adjustment and the Poor: Analytical Issues and Cross‐Country Evidence," Journal of Economic Surveys, Wiley Blackwell, vol. 18(3), pages 351-408, July.
    11. Atal, Vidya & Bar, Talia & Gordon, Sidartha, 2016. "Project selection: Commitment and competition," Games and Economic Behavior, Elsevier, vol. 96(C), pages 30-48.
    12. Yonggu Kim & Keeyoung Shin & Joseph Ahn & Eul-Bum Lee, 2017. "Probabilistic Cash Flow-Based Optimal Investment Timing Using Two-Color Rainbow Options Valuation for Economic Sustainability Appraisement," Sustainability, MDPI, vol. 9(10), pages 1-16, October.
    13. Bergendahl, Goran, 2005. "Models for investment in electronic commerce--financial perspectives with empirical evidence," Omega, Elsevier, vol. 33(4), pages 363-376, August.
    14. Prelipcean, Gabriela & Boscoianu, Mircea, 2019. "Aspect Regarding the Design of Active Strategies for Venture Capital Financing – the Flexible Adjustment for Romania as a Frontier Capital Market," Proceedings of the ENTRENOVA - ENTerprise REsearch InNOVAtion Conference (2019), Rovinj, Croatia, in: Proceedings of the ENTRENOVA - ENTerprise REsearch InNOVAtion Conference, Rovinj, Croatia, 12-14 September 2019, pages 187-196, IRENET - Society for Advancing Innovation and Research in Economy, Zagreb.
    15. Wong, Kit Pong, 2011. "Progressive taxation and the intensity and timing of investment," Economic Modelling, Elsevier, vol. 28(1-2), pages 100-108, January.
    16. Chahim, M. & Hartl, R.F. & Kort, P.M., 2011. "The Deterministic Impulse Control Maximum Principle in Operations Research : Necessary and Sufficient Optimality Conditions (replaces CentER DP 2011-052)," Discussion Paper 2011-133, Tilburg University, Center for Economic Research.
    17. Unterschultz, James R., 2000. "New Instruments For Co-Ordination And Risk Sharing Within The Canadian Beef Industry," Project Report Series 24046, University of Alberta, Department of Resource Economics and Environmental Sociology.
    18. Waters, James, 2015. "Optimal design and consequences of financial disclosure regulation: a real options approach," MPRA Paper 63369, University Library of Munich, Germany.
    19. Meade, Richard, 2006. "Valuing the Impact of Climate Change Policies on Forestry," Working Paper Series 19068, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    20. Yoon, Byung-Sam & Brorsen, B. Wade, 2005. "Can Multiyear Rollover Hedging Increase Mean Returns?," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 37(1), pages 65-78, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:08:y:2005:i:02:n:s0219024905002962. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.