On a PDE arising in one-dimensional stochastic control problems

The original publication is available at www.springerlink.comThe paper provides a systematic way for finding a partial differential equation that directly characterizes the optimal control, in the framework of onedimensional stochastic control problems of Mayer type, with no constraints on the controls. The results obtained are applied to continuous-time portfolio problems.We wish to thank an Associate Editor and two referees for helpful comments Both authors gratefully acknowledge financial support from the Spanish Ministerio de Ciencia e Innovación under project ECO2008-02358 The first author is also supported by Consejería de Educación de la Junta de Castilla y León (Spain) under project VA056A09Publicad