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BSDEs in utility maximization with BMO market price of risk

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  • Frei, Christoph
  • Mocha, Markus
  • Westray, Nicholas

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.

Suggested Citation

  • Frei, Christoph & Mocha, Markus & Westray, Nicholas, 2012. "BSDEs in utility maximization with BMO market price of risk," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2486-2519.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:6:p:2486-2519
    DOI: 10.1016/j.spa.2012.03.007
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    References listed on IDEAS

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