ISSN:
1572-9338
Keywords:
Incomplete market
;
trading constraints
;
linear programming
;
optimal portfolio
;
duality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract We study a consistent treatment for both the multi-period portfolio selection problem and the option attainability problem by a dual approach. We assume that time is discrete, the horizon is finite, the sample space is finite and the number of securities is less than that of the possible securities price transitions, i.e. an incomplete security market. The investor is prohibited from investing stocks more than given linear investment amount constraints at any time and he maximizes an expected additive utility function for the consumption process. First we give a set of budget feasibility conditions so that a consumption process is attainable by an admissible portfolio process. To establish this relation, we used an algorithmic approach which has a close connection with the linear programming duality. Then we prove the unique existence of a primal optimal solution from the budget feasibility conditions. Finally, we formulate a dual control problem and establish the duality between primal and dual control problems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02282058
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