Sublinear Expectations: On Large Sample Behaviours, Monte Carlo Method, and Coherent Upper Previsions

Abstract

Shige Peng’s sublinear expectations generalize ordinary linear expectation operators. It is shown that the behaviour of sample averages of Peng i.i.d. variables may be very different from the probabilistic intuition. In particular, Peng’s generalization of the Monte Carlo method is shown to be wrong. It is also observed that sublinear expectations coincide with Peter Walley’s coherent upper previsions on a linear space.