Skip to main content

Research Repository

Advanced Search

Time-randomized stopping problems for a family of utility functions



Huiling Le


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].


Pérez López, I., & Le, H. (2015). Time-randomized stopping problems for a family of utility functions. SIAM Journal on Control and Optimization, 53(3),

Journal Article Type Article
Acceptance Date Mar 9, 2015
Publication Date Jan 1, 2015
Deposit Date Apr 11, 2016
Publicly Available Date Apr 11, 2016
Journal SIAM Journal on Control and Optimization
Print ISSN 0363-0129
Electronic ISSN 1095-7138
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 53
Issue 3
Keywords optimal stopping, randomization, boundary value problem
Public URL
Publisher URL


Downloadable Citations