In this book, we take the notion of nonlinear expectation as a fundamental notion of an
axiomatical system. This enables us to get directly many new and fundamental results: such …

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We consider the problem of superhedging under volatility uncertainty for an investor allowed
to dynamically trade the underlying asset, and statically trade European call options for all …

We provide an existence and uniqueness theory for an extension of backward SDEs to the
second order. While standard Backward SDEs are naturally connected to semilinear PDEs …

We formulate a model of utility for a continuous-time framework that captures aversion to
ambiguity about both volatility and drift. Corresponding extensions of some basic results in …

We consider a general formulation of the principal–agent problem with a lump-sum payment
on a finite horizon, providing a systematic method for solving such problems. Our approach …

This paper considers the nonlinear theory of G-martingales as introduced by Peng (2007) in
[16, 17]. A martingale representation theorem for this theory is proved by using the …

This paper formulates a model of utility for a continuous time framework that captures the
decision-maker's concern with ambiguity about both the drift and volatility of the driving …

We provide a general construction of time-consistent sublinear expectations on the space of
continuous paths. It yields the existence of the conditional G-expectation of a Borel …

We consider a contracting problem in which a principal hires an agent to manage a risky
project. When the agent chooses volatility components of the output process and the …