Research Repository

# Time-randomized stopping problems for a family of utility functions

## Authors

Iker Pérez López ikertxo1986@gmail.com

HUILING LE huiling.le@nottingham.ac.uk
Professor of Probability

### 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), doi:10.1137/130946800

Journal Article Type Article Mar 9, 2015 Jan 1, 2015 Apr 11, 2016 Apr 11, 2016 SIAM Journal on Control and Optimization 0363-0129 1095-7138 Society for Industrial and Applied Mathematics Peer Reviewed 53 3 https://doi.org/10.1137/130946800 optimal stopping, randomization, boundary value problem http://eprints.nottingham.ac.uk/id/eprint/32709 http://epubs.siam.org/doi/10.1137/130946800 Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

#### Files

published.pdf (627 Kb)
PDF