In this paper a simple problem of combined singular stochastic control and optimal stopping is formulated and solved. We find that the optimal strategies can take qualitatively different forms, depending on parameter values. We also study a variant on the problem in which the value function is inherently nonconvex. The proofs employ the generalised Ito formula applicable for differences of convex functions.
Publié le : 1994-02-14
Classification:
Singular stochastic control,
optimal stopping,
Brownian motion,
local time,
reflecting diffusions,
93E20,
60G40,
60J65
@article{1177005209,
author = {Davis, M. H. A. and Zervos, M.},
title = {A Problem of Singular Stochastic Control with Discretionary Stopping},
journal = {Ann. Appl. Probab.},
volume = {4},
number = {4},
year = {1994},
pages = { 226-240},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005209}
}
Davis, M. H. A.; Zervos, M. A Problem of Singular Stochastic Control with Discretionary Stopping. Ann. Appl. Probab., Tome 4 (1994) no. 4, pp. 226-240. http://gdmltest.u-ga.fr/item/1177005209/