Robust Utility Maximization in Non-Dominated Models with 2BSDE: The Uncertain Volatility Model
Possamaï, Dylan; Zhou, Chao; Matoussi, Anis (2015), Robust Utility Maximization in Non-Dominated Models with 2BSDE: The Uncertain Volatility Model, Mathematical Finance, 25, 2, p. 258-287. http://dx.doi.org/10.1111/mafi.12031
TypeArticle accepté pour publication ou publié
Journal nameMathematical Finance
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Abstract (EN)The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is nondominated. We propose studying this problem in the framework of second-order backward stochastic differential equations (2BSDEs for short) with quadratic growth generators. We show for exponential, power, and logarithmic utilities that the value function of the problem can be written as the initial value of a particular 2BSDE and prove existence of an optimal strategy. Finally, several examples which shed more light on the problem and its links with the classical utility maximization one are provided. In particular, we show that in some cases, the upper bound of the volatility interval plays a central role, exactly as in the option pricing problem with uncertain volatility models.
Subjects / Keywordsquadratic growth; robust utility maximization; volatility uncertainty; second-order backward stochastic differential equation
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Corrigendum for "Second-order reflected backward stochastic differential equations" and "Second-order BSDEs with general reflection and game options under uncertainty" Matoussi, Anis; Possamaï, Dylan; Zhou, Chao (2021) Article accepté pour publication ou publié