Time-randomized stopping problems for a family of utility functions
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...
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| Format: | Article |
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Society for Industrial and Applied Mathematics
2015
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| Online Access: | https://eprints.nottingham.ac.uk/32709/ |
| _version_ | 1848794472769388544 |
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| author | Pérez López, Iker Le, Huiling |
| author_facet | Pérez López, Iker Le, Huiling |
| author_sort | Pérez López, Iker |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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]. |
| first_indexed | 2025-11-14T19:16:44Z |
| format | Article |
| id | nottingham-32709 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:16:44Z |
| publishDate | 2015 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-327092020-05-04T20:11:46Z https://eprints.nottingham.ac.uk/32709/ Time-randomized stopping problems for a family of utility functions Pérez López, Iker Le, Huiling 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]. Society for Industrial and Applied Mathematics 2015 Article PeerReviewed Pérez López, Iker and Le, Huiling (2015) Time-randomized stopping problems for a family of utility functions. SIAM Journal on Control and Optimization, 53 (3). pp. 1328-1345. ISSN 1095-7138 optimal stopping randomization boundary value problem http://epubs.siam.org/doi/10.1137/130946800 doi:10.1137/130946800 doi:10.1137/130946800 |
| spellingShingle | optimal stopping randomization boundary value problem Pérez López, Iker Le, Huiling Time-randomized stopping problems for a family of utility functions |
| title | Time-randomized stopping problems for a family of utility functions |
| title_full | Time-randomized stopping problems for a family of utility functions |
| title_fullStr | Time-randomized stopping problems for a family of utility functions |
| title_full_unstemmed | Time-randomized stopping problems for a family of utility functions |
| title_short | Time-randomized stopping problems for a family of utility functions |
| title_sort | time-randomized stopping problems for a family of utility functions |
| topic | optimal stopping randomization boundary value problem |
| url | https://eprints.nottingham.ac.uk/32709/ https://eprints.nottingham.ac.uk/32709/ https://eprints.nottingham.ac.uk/32709/ |