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Stochastic optimization under constraints

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  • Mnif, Mohammed
  • Pham, Huyên

Abstract

We study a stochastic optimization problem under constraints in a general framework including financial models with constrained portfolios, labor income and large investor models and reinsurance models. We also impose American-type constraint on the state space process. General objective functions including deterministic or random utility functions and shortfall risk loss functions are considered. We first prove existence and uniqueness result to this optimization problem. In a second part, we develop a dual formulation under minimal assumptions on the objective functions, which are the analogue of the asymptotic elasticity condition of Kramkov and Schachermayer (1999).

Suggested Citation

  • Mnif, Mohammed & Pham, Huyên, 2001. "Stochastic optimization under constraints," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 149-180, May.
    • Handle: RePEc:eee:spapps:v:93:y:2001:i:1:p:149-180
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    References listed on IDEAS

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    6. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
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    8. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
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    Cited by:

    1. Leonel Perez-hernandez, 2007. "On the existence of an efficient hedge for an American contingent claim within a discrete time market," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 547-551.
    2. Kasper Larsen & Gordan v{Z}itkovi'c, 2011. "On utility maximization under convex portfolio constraints," Papers 1102.0346, arXiv.org, revised Feb 2013.
    3. Markus Mocha & Nicholas Westray, 2011. "The Stability of the Constrained Utility Maximization Problem - A BSDE Approach," Papers 1107.0190, arXiv.org.
    4. Nicholas Westray & Harry Zheng, 2010. "Constrained NonSmooth Utility Maximization on the Positive Real Line," Papers 1010.4055, arXiv.org.
    5. Wahid Faidi & Hanen Mezghanni & Mohamed Mnif, 2019. "Expected Utility Maximization Problem Under State Constraints and Model Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1123-1152, December.

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