Robust utility maximization with extremely ambiguity-loving and ambiguity-aversion preferences

Abstract

In this paper, we investigate the robust utility maximization problems under both preferences of extremely ambiguity loving and ambiguity aversion. By a fundamental martingale characterization technique on nonlinear expectations, optimal investment strategies are explicitly solved in a general non-Markovian framework via backward stochastic differential equations. Different with previous works in the literature assuming the convexity of the set of prior probability measures , our analysis are independent of the cardinality of . Our results show that extremely ambiguity-loving (resp. -aversion) investors will adopt the extremely aggressive (resp. conservative) investment strategy.

Keywords:

• Ambiguity
• backward stochastic differential equations
• martingale characterization
• robust utility maximization
• nonlinear expectations

Notes

No potential conflict of interest was reported by the authors.

1 Recently, in the spirit of -MEU, Beissner et al. [1] introduced an analogy called ‘dynamic consistent –MEU’ and provided its BSDE characterization.

Additional information

Funding

Bin Li gratefully acknowledges the support from a grant from Natural Sciences and Engineering Research Council of Canada [grant number 05828] and a start-up grant from the University of Waterloo. Dewen Xiong acknowledges the support from a grant from National Natural Science Foundation of China [grant number 11671257], a grant from Natural Science of Shanghai [grant number 13ZR1422000], and Shanghai 085 Project.