Optimal Stopping for Partial Sums
Darling, D. A. ; Liggett, T. ; Taylor, H. M.
Ann. Math. Statist., Tome 43 (1972) no. 6, p. 1363-1368 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We determine $\sup E\lbrack r(S_T)\rbrack$, where $S_n$ is a sequence of partial sums of independent identically distributed random variables, for two reward functions: $r(x) = x^+$ and $r(x) = (e^x - 1)^+$. The supremum is taken over all stop rules $T$. We give conditions under which the optimal expected return is finite. Under these conditions, optimal stopping times exist, and we determine them. The problem has an interpretation in an action timing problem in finance.
Publié le : 1972-08-14
Classification:  
@article{1177692491,
     author = {Darling, D. A. and Liggett, T. and Taylor, H. M.},
     title = {Optimal Stopping for Partial Sums},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 1363-1368},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692491}
}

Darling, D. A.; Liggett, T.; Taylor, H. M. Optimal Stopping for Partial Sums. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  1363-1368. http://gdmltest.u-ga.fr/item/1177692491/