Optimal consumption and arbitrage in incomplete, finite state security markets
The paper introduces a discrete time, finite horizon and finite security market models, and formulates the optimal consumption and portfolio selection problem. Necessary and sufficient budget feasibility conditions are derived in order to guarantee attainability of a consumption process by an admissible portfolio process. Existence of a unique optimal primal control process is established under primal and dual feasibility. The duality between the original consumption and portfolio selection problem and its associated dual problem is demonstrated. As opposed to \textit{J. Cvitanic} and \textit{I. Karantzas} [Ann. Appl. Prob. 2, No. 4, 767-818 (1992)], who impose an investment rate restriction, the present paper employs restrictions on the stock investment amount.
optimal consumption and portfolio selection
scientific article; zbMATH DE number 490529
scientific article