In this article, we study the problem of robust utility maximization in an incomplete market with volatility uncertainty. The set of all possible models (probability measures) considered here is non-dominated. We propose to study this problem in the framework of second order backward stochastic differential equations introduced in Soner, Touzi and Zhang (2010) for Lipschitz continuous generator, then generalized by Possamai and Zhou (2011) in the quadratic growth case. We solve the problem for exponential, power and logarithmic utility functions and prove existence of an optimal strategy and of an optimal probability measure . Finally we provide several examples which shed more light and intuitions on the problem and its links with the classical utility maximisation one.
In this article, we consider the problem of robust utility maximization in an incomplete market with volatility uncertainty. The set of all possible models (probability measures) considered here is non-dominated. We propose to study this problem in the framework of second order backward stochastic differential equations introduced in Soner, Touzi and Zhang (2010) for Lipschitz continuous generator, then generalized by Possamai and Zhou (2011) in the quadratic growth case. We solve the problem for exponential, power and logarithmic utility functions and prove existence of an optimal strategy . Finally we provide several examples which shed more light on the problem and its links with the classical utility maximization one.
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