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Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem

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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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Authors and Affiliations

  1. Université du Maine, Avenue Olivier Messiaen, 72085, Le Mans, France

    Marie-Amélie Morlais

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  1. Marie-Amélie Morlais
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Correspondence to Marie-Amélie Morlais.

Additional information

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

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