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Stochastic optimization under constraints

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  • Mnif, Mohammed
  • Pham, Huyên
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    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).

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 93 (2001)
    Issue (Month): 1 (May)
    Pages: 149-180

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    Handle: RePEc:eee:spapps:v:93:y:2001:i:1:p:149-180

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    Related research

    Keywords: Stochastic optimization Convex and state constraints Optional decomposition Duality theory Finance and insurance;

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    1. Domenico Cuoco & Jaksa Cvitanic, . "Optimal Consumption Choices for a "Large" Investor," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 04-96, Wharton School Rodney L. White Center for Financial Research.
    2. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. 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.
    4. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
    5. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    6. Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
    7. He, Hua & Pages, Henri F, 1993. "Labor Income, Borrowing Constraints, and Equilibrium Asset Prices," Economic Theory, Springer, vol. 3(4), pages 663-96, October.
    8. repec:wop:humbsf:1997-31 is not listed on IDEAS
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