We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in the price impact model developed by Bank and Kramkov (2011) [1,2]. These conditions are stated as smoothness and boundedness requirements on utility functions or...

We give a new and comparably short proof of Gittins' index theorem for dynamic allocation problems of the multi-armed bandit type in continuous time under minimal assumptions. This proof gives a complete characterization of optimal allocation strategies as those policies which follow the current...

This paper considers the nonlinear theory of G-martingales as introduced by Peng (2007) in [16] and [17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in Soner et al. (2009) [20] for the second-order stochastic target...

We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng’s G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian...