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On a PDE Arising in One-Dimensional Stochastic Control Problems

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Abstract

The paper provides a systematic way for finding a partial differential equation that directly characterizes the optimal control, in the framework of one-dimensional stochastic control problems of Mayer type, with no constraints on the controls. The results obtained are applied to continuous-time portfolio problems.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de Valladolid, 47005, Paseo Prado de la Magdalena s/n, Valladolid, Spain

    Ricardo Josa-Fombellida

  2. Departamento de Economía, Universidad Carlos III de Madrid, 28903, C/Madrid 126, Getafe, Madrid, Spain

    Juan Pablo Rincón-Zapatero

Authors
  1. Ricardo Josa-Fombellida
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  2. Juan Pablo Rincón-Zapatero
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Corresponding author

Correspondence to Juan Pablo Rincón-Zapatero.

Additional information

Communicated by H.J. Pesch.

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 VA056A09.

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Josa-Fombellida, R., Rincón-Zapatero, J.P. On a PDE Arising in One-Dimensional Stochastic Control Problems. J Optim Theory Appl 147, 1–26 (2010). https://doi.org/10.1007/s10957-010-9712-3

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  • DOI: https://doi.org/10.1007/s10957-010-9712-3

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