| Affiliation: | (1) Université de Franche-Comté, 16 Route de Gray, 25030 Besançon Cedex, France;(2) Central Economics and Mathematics Institute, Moscow, Russia;(3) Center for Mathematical Sciences, Munich University of Technology, Boltzmannstrasse 3, 85747 Garching bei München, Germany |
| Abstract: | We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique viscosity solution of a HJB equation.Mathematics Subject Classification (1991): 60G44JEL Classification: G13, G11This research was done at Munich University of Technology supported by a Mercator Guest Professorship of the German Science Foundation (Deutsche Forschungsgemeinschaft). The authors also express their thanks to Mark Davis, Steve Shreve, and Michael Taksar for useful discussions concerning the principle of dynamic programming. |
