@article { ,
title = {Time-randomized stopping problems for a family of utility functions},
abstract = {This paper studies stopping problems of the form \$V=\\inf\_\{0 \\leq \\tau \\leq T\} \\mathbb\{E\}[U(\\frac\{\\max\_\{0\\le s \\le T\} Z\_s \}\{Z\_\\tau\})]\$ for strictly concave or convex utility functions U in a family of increasing functions satisfying certain conditions, where Z is a geometric Brownian motion and T is the time of the nth jump of a Poisson process independent of Z. We obtain some properties of \$V\$ and offer solutions for the optimal strategies to follow. This provides us with a technique to build numerical approximations of stopping boundaries for the fixed terminal time optimal stopping problem presented in [J. Du Toit and G. Peskir, Ann. Appl. Probab., 19 (2009), pp. 983--1014].},
doi = {10.1137/130946800},
eissn = {1095-7138},
issn = {0363-0129},
issue = {3},
journal = {SIAM Journal on Control and Optimization},
publicationstatus = {Published},
publisher = {Society for Industrial and Applied Mathematics},
url = {https://nottingham-repository.worktribe.com/output/992883},
volume = {53},
keyword = {optimal stopping, randomization, boundary value problem},
year = {2015},
author = {Pérez López, Iker and Le, Huiling}
}