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Pricing Via Utility Maximization and Entropy[Note 1. The authors thank Monique Jeanblanc for her careful reading, ...]
Author(s) -
Rouge Richard,
El Karoui Nicole
Publication year - 2000
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 - 10.1111/1467-9965.00093
Subject(s) - portfolio , utility maximization , mathematical economics , economics , quadratic equation , exponential utility , maximization , exponential function , bellman equation , mathematics , econometrics , financial economics , microeconomics , mathematical analysis , geometry
In a financial market model with constraints on the portfolios, define the price for a claim C as the smallest real number p such that sup π E[ U ( X T x + p , π − C )]≥ sup π E[ U ( X T x , π )], where U is the negative exponential utility function and X x , π is the wealth associated with portfolio π and initial value x . We give the relations of this price with minimal entropy or fair price in the flavor of Karatzas and Kou (1996) and superreplication. Using dynamical methods, we characterize the price equation, which is a quadratic Backward SDE, and describe the optimal wealth and portfolio. Further use of Backward SDE techniques allows for easy determination of the pricing function properties.