Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption

Abstract

We consider a problem of optimal investment with intermediate consumption in the framework of an incomplete semimartingale model of a financial market. We show that a necessary and sufficient condition for the validity of key assertions of the theory is that the value functions of the primal and dual problems are finite. Thesis Advisor: Professor Dmitry Kramkov AcknowledgementsFirst and foremost, I would like to thank my advisor Dmitry Kramkov. He has systematically challenged me to consider the most general case in which one still can hope to achieve a result. Dmitry has helped me to overcome difficulties with his advice and provided critical insights and suggestions at the right moments. Studying and discussing with him, in particular his papers, gave me an idea of how central mathematical results are developed and helped to perform on my (local) maximum.I would also like to thank Steven Shreve for teaching so much through his books and our conversations. Many other professors in the department have given me invaluable instruction and advice, including

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