Iker P�rez L�pez
Time-randomized stopping problems for a family of utility functions
P�rez L�pez, Iker; Le, Huiling
Authors
Huiling Le
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].
Citation
Pérez López, I., & Le, H. (2015). Time-randomized stopping problems for a family of utility functions. SIAM Journal on Control and Optimization, 53(3), https://doi.org/10.1137/130946800
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 |
DOI | https://doi.org/10.1137/130946800 |
Keywords | optimal stopping, randomization, boundary value problem |
Public URL | https://nottingham-repository.worktribe.com/output/992883 |
Publisher URL | http://epubs.siam.org/doi/10.1137/130946800 |
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