Investment Optimization under Constraints

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Investment Optimization under Constraints

Author Info

Long Nguyen-Thanh (Warsaw School of Economics - Department of Management and Finance)

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Long Nguyen-Thanh

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).

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Paper provided by EconWPA in its series Finance with number 0301005.

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Length: 26 pages
Date of creation: 09 Jan 2003
Date of revision: 10 Jan 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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Find related papers by JEL classification:
G - Financial Economics

This paper has been announced in the following NEP Reports:

NEP-ALL-2003-01-12 (All new papers)
NEP-CFN-2003-01-12 (Corporate Finance)
NEP-CWA-2003-01-12 (Central & Western Asia)
NEP-MFD-2003-01-12 (Microfinance)
NEP-RMG-2003-01-12 (Risk Management)

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Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440. [Downloadable!] (restricted)
Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany. [Downloadable!]
R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
Other versions:
- 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. [Downloadable!] (restricted)
H. Föllmer & D. Kramkov, . "Optional decompositions under constraints," Sonderforschungsbereich 373 1997-31, Humboldt Universitaet Berlin.

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