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OPTIMAL INVESTMENT WITH INTERMEDIATE CONSUMPTION AND RANDOM ENDOWMENT
Author(s) -
Mostovyi Oleksii
Publication year - 2017
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12089
Subject(s) - semimartingale , endowment , economics , utility maximization problem , consumption (sociology) , investment (military) , incomplete markets , mathematical economics , econometrics , microeconomics , maximization , value (mathematics) , terminal value , expected utility hypothesis , maturity (psychological) , utility maximization , financial economics , mathematics , net present value , production (economics) , statistics , psychology , social science , philosophy , developmental psychology , epistemology , sociology , politics , political science , law
We consider an optimal investment problem with intermediate consumption and random endowment, in an incomplete semimartingale model of the financial market. We establish the key assertions of the utility maximization theory, assuming that both primal and dual value functions are finite in the interiors of their domains and that the random endowment at maturity can be dominated by the terminal value of a self‐financing wealth process. In order to facilitate the verification of these conditions, we present alternative, but equivalent conditions, under which the conclusions of the theory hold.