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- Title
OPTIMAL STOPPING FOR THE LAST EXIT TIME.
- Authors
REN, DAN
- Abstract
Given a one-dimensional downwards transient diffusion process $X$ , we consider a random time $\unicode[STIX]{x1D70C}$ , the last exit time when $X$ exits a certain level $\ell$ , and detect the optimal stopping time for it. In particular, for this random time $\unicode[STIX]{x1D70C}$ , we solve the optimisation problem $\inf _{\unicode[STIX]{x1D70F}}\mathbb{E}[\unicode[STIX]{x1D706}(\unicode[STIX]{x1D70F}-\unicode[STIX]{x1D70C})_{+}+(1-\unicode[STIX]{x1D706})(\unicode[STIX]{x1D70C}-\unicode[STIX]{x1D70F})_{+}]$ over all stopping times $\unicode[STIX]{x1D70F}$. We show that the process should stop optimally when it runs below some fixed level $\unicode[STIX]{x1D705}_{\ell }$ for the first time, where $\unicode[STIX]{x1D705}_{\ell }$ is the unique solution in the interval $(0,\unicode[STIX]{x1D706}\ell)$ of an explicitly defined equation.
- Subjects
OPTIMAL stopping (Mathematical statistics); MATHEMATICAL models of diffusion; MATHEMATICAL functions; EQUATIONS; MATHEMATICS theorems
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p148
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718000990