Abstract
In this paper, we study a class of quadratic backward stochastic differential equations (BSDEs), which arises naturally in the utility maximization problem with portfolio constraints. We first establish the existence and uniqueness of solutions for such BSDEs and then give applications to the utility maximization problem. Three cases of utility functions, the exponential, power, and logarithmic ones, are discussed.
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This study is part of my PhD thesis supervised by Professor Ying Hu and defended at the University of Rennes 1 (in France) in October 2007.
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Morlais, MA. Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem. Finance Stoch 13, 121–150 (2009). https://doi.org/10.1007/s00780-008-0079-3
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DOI: https://doi.org/10.1007/s00780-008-0079-3
Keywords
- Backward stochastic differential equations (BSDEs)
- Continuous filtration
- Quadratic growth
- Utility maximization
- Portfolio constraints