Geodesic
On one problem of the optimal choice of record values
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 30-37

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Independent random variables $X_1,X_2,\dots, X_n$ having $\mathrm U([0,1])$-uniform distribution and the upper record values in this set are considered. We study the problem how to maximize (taking into account some consecutively observed values $x_1,x_2,\dots,x_k$ of these $X$-s) the expectation of sums of records in this sequence under the optimal choice of the corresponding variable $X_k$ (instead of $X_1$) as the initial record value. 
@article{ZNSL_2017_466_a1,
     author = {I. V. Bel'kov and V. B. Nevzorov},
     title = {On one problem of the optimal choice of record values},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {30--37},
     publisher = {mathdoc},
     volume = {466},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a1/}
}
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I. V. Bel'kov; V. B. Nevzorov. On one problem of the optimal choice of record values. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 30-37. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a1/