BSDEs in Utility Maximization with BMO Market Price of Risk

Christoph Frei, Markus Mocha and Nicholas Westray

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Abstract: This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. This feature occurs since, contrary to the classical Ito representation theorem, a representation of random variables in terms of stochastic exponentials is not unique. We study in detail when the BSDE has a bounded solution and derive a new dynamic exponential moments condition which is shown to be the minimal sufficient condition in a general filtration. The main results are complemented by several interesting examples which illustrate their sharpness as well as important properties of the utility maximization BSDE.

Date: 2011-07, Revised 2012-02
New Economics Papers: this item is included in nep-upt
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Published in Stochastic Process. Appl., 122 (6): 2486 - 2519, 2012

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1107.0183

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