Geodesic
The optimal stopping of an integral with respect to the Wiener process
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 397-401

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In this paper an optimal bound is found in the stopping problem, for the Wiener process $W_t$, $0\le t\le1$, with gain $$ V(0,x)=\sup_{0\le\tau\le1}\mathbf M\int_0^\tau(W_s+x)\,ds, $$ where $\tau$ is a Markov time with respect to the family of $\sigma$-algebras $\mathscr F_t^W=\sigma\{W_s,s\le t\}$. 
@article{TVP_1975_20_2_a14,
     author = {T. P. Miroshnichenko},
     title = {The optimal stopping of an integral with respect to the {Wiener} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {397--401},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a14/}
}
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T. P. Miroshnichenko. The optimal stopping of an integral with respect to the Wiener process. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 397-401. http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a14/