Geodesic
Optimal local first exit time
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 83-108

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A random process and the corresponding class of so called local first exit times are considered. For a special functional depending on Markov times the problem to find the optimal one is investigated. A description of the class is obtained. For diffusion Markov processes the folowing alternative is proved: either the global first exit time is optimal (trivial case), or in the given class there are no optimal Markov times. For a non-Markov piece-wise increasing process a non-trivial example of the local first exit time is constructed. An application of the problem to insurance is discussed. Bibl. – 7 titles. 
@article{ZNSL_2008_361_a6,
     author = {S. S. Rasova and B. P. Harlamov},
     title = {Optimal local first exit time},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {83--108},
     publisher = {mathdoc},
     volume = {361},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a6/}
}
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S. S. Rasova; B. P. Harlamov. Optimal local first exit time. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 83-108. http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a6/