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Investment Optimization under Constraints

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  • Long Nguyen-Thanh

    (Warsaw School of Economics - Department of Management and Finance)

Abstract

We analyze general stochastic optimization financial problems under constraints in a general framework, which includes financial models with some ``imperfection'', such as constrained portfolios, labor income, random endowment and large investor models. By using general optional decomposition under constraints in a multiplicative form, we first develop a dual formulation under minimal assumption modeled as in Pham and Mnif (2002), Long (2002). We then are able to prove an existence and uniqueness of an optimal solution to primal and to the corresponding dual problem. An optimal investment to the original problem then can be found by convex duality, similarly to the case considered by Kramkov and Schachermayer (1999).

Suggested Citation

  • Long Nguyen-Thanh, 2003. "Investment Optimization under Constraints," Finance 0301005, University Library of Munich, Germany, revised 09 Mar 2003.
    • Handle: RePEc:wpa:wuwpfi:0301005
    Note: Type of Document - Tex/PDF; prepared on IBM PC - PC-TEX/UNIX Sparc TeX; to print on HP/PostScript/Franciscan monk; pages: 26; figures: no figure
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    References listed on IDEAS

    as
    1. Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
    2. 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.
    3. 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.
    4. I. Klein & L. C. G. Rogers, 2007. "Duality In Optimal Investment And Consumption Problems With Market Frictions," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 225-247, April.
    5. Domenico Cuoco & Hong Liu, 2000. "A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 355-385, July.
    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.
    7. 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.
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    Cited by:

    1. Hugo E. Ramirez & Rafael Serrano, 2023. "Optimal investment with insurable background risk and nonlinear portfolio allocation frictions," Papers 2303.04236, arXiv.org.
    2. Ramírez, H & Serrano, R, 2023. "Optimal investment with insurable background risk and nonlinear portfolio allocation frictions," Documentos de Trabajo 20658, Universidad del Rosario.

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    More about this item

    Keywords

    Stochastic Optimization; Investment Optimization; Duality Theory; Convex and State Constraints; Optional Decomposition;
    All these keywords.

    JEL classification:

    • G - Financial Economics

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