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).
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Paper provided by EconWPA in its series Finance with number
0211004.
Length: 31 pages Date of creation: 19 Nov 2002 Date of revision:
19 Nov 2002 Handle: RePEc:wpa:wuwpfi:0211004
Note: Type of Document - Tex/PDF; prepared on IBM PC - PC-TEX/UNIX Sparc TeX; to print on HP/PostScript/Franciscan monk; pages: 31 Contact details of provider: Web page: http://129.3.20.41
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