Optimal time to invest when the price processes are geometric Brownian motions. A tentative based on smooth fit
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.
|Date of creation:||01 Jul 2011|
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- 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.
- 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.
- Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
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