BSDEs in utility maximization with BMO market price of risk

Christoph Frei, Markus Mocha and Nicholas Westray

Stochastic Processes and their Applications, 2012, vol. 122, issue 6, 2486-2519

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 Itô 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.

Keywords: Quadratic BSDEs; BMO market price of risk; Power utility maximization; Dynamic exponential moments (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:6:p:2486-2519

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DOI: 10.1016/j.spa.2012.03.007

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