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On a PDE Arising in One-Dimensional Stochastic Control Problems

Author

Listed:
  • Ricardo Josa-Fombellida

    (Universidad de Valladolid)

  • Juan Pablo Rincón-Zapatero

    (Universidad Carlos III de Madrid)

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.

Suggested Citation

  • Ricardo Josa-Fombellida & Juan Pablo Rincón-Zapatero, 2010. "On a PDE Arising in One-Dimensional Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 1-26, October.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:1:d:10.1007_s10957-010-9712-3
    DOI: 10.1007/s10957-010-9712-3
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    References listed on IDEAS

    as
    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    3. Ioannis Karatzas & John P. Lehoczky & Suresh P. Sethi & Steven E. Shreve, 1986. "Explicit Solution of a General Consumption/Investment Problem," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 261-294, May.
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