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A note on explicit bounds for a stopped Feynman-Kac functional

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  • Makasu, Cloud

Abstract

Let Qt=(xt,yt) be a two-dimensional geometric Brownian motion which is possibly correlated starting at (x,y) in the positive quadrant, and let [tau] be an -stopping time generated by the process Qt. Under certain conditions, we prove that where [Phi] is a bounded Borel function, C>0, [mu]>1, n>1 are constants and g* is an explicit bound for a solution of a certain second order ordinary differential equation. The present result extends and supplements the explicit upper bound in Hu and Øksendal (1998).

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  • Makasu, Cloud, 2010. "A note on explicit bounds for a stopped Feynman-Kac functional," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1977-1979, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1977-1979
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    References listed on IDEAS

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    1. 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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