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Controlling a stopped diffusion process to reach a goal

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  • Makasu, Cloud

Abstract

We consider a problem of optimally controlling a two-dimensional diffusion process initially starting in the interior of a domain until it reaches the line y=[theta][phi](x) at a stopping time [tau] 0 and [theta]>1 are fixed positive constants and [phi](x) is a given positive strictly increasing, twice continuously differentiable function on (0,[infinity]) such that [phi](0)>=0. The goal is to maximize the probability criterion over a class of admissible controls consisting of bounded, Borel measurable functions. Under suitable conditions, it is shown that the maximal probability is given explicitly and the optimal process is determined explicitly by

Suggested Citation

  • Makasu, Cloud, 2010. "Controlling a stopped diffusion process to reach a goal," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1218-1222, August.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:15-16:p:1218-1222
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    References listed on IDEAS

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    1. Victor C. Pestien & William D. Sudderth, 1988. "Continuous-Time Casino Problems," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 364-376, May.
    2. Victor C. Pestien & William D. Sudderth, 1985. "Continuous-Time Red and Black: How to Control a Diffusion to a Goal," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 599-611, November.
    3. Makasu, Cloud, 2008. "On mean exit time from a curvilinear domain," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2859-2863, December.
    4. William D. Sudderth & Ananda Weerasinghe, 1989. "Controlling a Process to a Goal in Finite Time," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 400-409, August.
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