Consumption and Investment Optimization under Constraints

Long Nguyen-Thanh

Finance from EconWPA

Abstract: We analyze a problem of maximization of expected terminal wealth and consumption under constraints in a general framework including financial models with constrained portfolios, labor income 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). 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 and consumption plan to the original problem then can be found by convex duality, similarly to the case considered by Kramkov and Schachermayer (1999).

Keywords: Stochastic Optimization; Consumption and Investment Optimization; Duality Theory; Convex and State Constraints; Utility Maximization; Optional Decomposition; Minimax Theorem} (search for similar items in EconPapers)
JEL-codes: G (search for similar items in EconPapers)
Date: 2002-11-19, Revised 2003-03-25
Note: Type of Document - Tex/PDF; prepared on IBM PC - PC-TEX/UNIX Sparc TeX; to print on HP/PostScript/Franciscan monk; pages: 31
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0211004

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