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- Publisher
- Springer Journals
- Copyright
- Copyright © 2001 by Springer-Verlag Berlin Heidelberg & EMS
- Subject
- Mathematics; Mathematics, general
- ISSN
- 1435-9855
- DOI
- 10.1007/s100970100039
- Publisher site
- See Article on Publisher Site
Abstract
Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process can be driven into a target set at a specified time. Differential properties of these sets are studied by the dynamic programming principle which is proved by the Jankov-von Neumann measurable selection theorem. This principle implies that the reachability sets satisfy a geometric partial differential equation, which is the analogue of the Hamilton-Jacobi-Bellman equation for this problem. By appropriately choosing the controlled process, this connection provides a stochastic representation for mean curvature type geometric flows. Another application is the super-replication problem in financial mathematics. Several applications in this direction are also discussed.
Journal
Journal of the European Mathematical Society – Springer Journals
Published: Sep 1, 2002