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Optimal Investment Strategy Via Interval Arithmetic

Author

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  • 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
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    References listed on IDEAS

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    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
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    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.

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