Geodesic
Dynamic programming for stochastic target problems and geometric flows
Journal of the European Mathematical Society, Tome 4 (2002) no. 3, pp. 201-236 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.1007/s100970100039
Classification : 49-XX, 35-XX, 60-XX, 00-XX
Keywords: 
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     author = {H. Mete Soner and Nizar Touzi},
     title = {Dynamic programming for stochastic target problems and geometric flows},
     journal = {Journal of the European Mathematical Society},
     pages = {201--236},
     year = {2002},
     volume = {4},
     number = {3},
     doi = {10.1007/s100970100039},
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H. Mete Soner; Nizar Touzi. Dynamic programming for stochastic target problems and geometric flows. Journal of the European Mathematical Society, Tome 4 (2002) no. 3, pp. 201-236. doi: 10.1007/s100970100039

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