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On mean exit time from a curvilinear domain

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  • Makasu, Cloud

Abstract

In this short communication, we consider a mean exit time problem for a non-degenerate, two-dimensional, coupled diffusion process Mt=(xt,yt) in the interior of a curvilinear domain with a C2-boundary, where xt is any arbitrary diffusion process and yt is a geometric Brownian motion evolving under non-explosive conditions, and [psi](.) is a real-valued, positive, increasing, continuous function such that [psi](0)>=0. It is proved that, under certain conditions, the mean exit time is a logarithmic function associated with a certain second-order nonlinear ordinary differential equation. At the end of the note, we shall present several examples to illustrate our main result.

Suggested Citation

  • Makasu, Cloud, 2008. "On mean exit time from a curvilinear domain," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2859-2863, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2859-2863
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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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    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Guo, Zhi Jun, 2008. "A note on the CIR process and the existence of equivalent martingale measures," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 481-487, April.
    5. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    1. Makasu, Cloud, 2010. "Controlling a stopped diffusion process to reach a goal," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1218-1222, August.

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