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Optimal time to invest when the price processes are geometric Brownian motions. A tentative based on smooth fit

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  • GAHUNGU, Joachim

    ()
    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • SMEERS, Yves

    ()
    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

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    Abstract

    This paper considers the problem of the optimal timing of the exchange of the sum of n geometric Brownian motions for the sum of m others. We propose a closed form determinable stopping time based on the heuristic principle of smooth fit. We cannot prove that this stopping time is optimal. However, we show numerically on examples that it is a potentially useful candidate: letting S^Ø denote the stopping region induced by our stopping time we show that (i) S^- c S^Ø c S^+ where S^- and S^+ are well-known subset and superset of the optimal stopping region; (ii) stopping at the first entry time of S^Ø offers a better payoff than stopping at the first entry time of S^- or S^+, especially when assets are correlated.

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    File URL: http://uclouvain.be/cps/ucl/doc/core/documents/coredp2011_34web.pdf
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    Bibliographic Info

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2011034.

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    Date of creation: 01 Jul 2011
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    Handle: RePEc:cor:louvco:2011034

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    Related research

    Keywords: optimal stopping; geometric Brownian motion; smooth fit;

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    1. Olsen, Trond E. & Stensland, Gunnar, 1992. "On optimal timing of investment when cost components are additive and follow geometric diffusions," Journal of Economic Dynamics and Control, Elsevier, vol. 16(1), pages 39-51, January.
    2. McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 707-27, November.
    3. Yaozhong Hu & Bernt Øksendal, 1998. "Optimal time to invest when the price processes are geometric Brownian motions," Finance and Stochastics, Springer, vol. 2(3), pages 295-310.
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