In this paper, we give the extensions of Peng's g-expectations which are called generalized Peng's g-expectations and investigate their related properties. Furthermore, we prove the stability theorem of generalized Peng's g-expectations.

Buckdahn et al. (2009b) introduced a mean-field stochastic differential equation to study the backward stochastic differential equation. The objective of the present paper is to deepen the investigation of such mean-field stochastic differential equations by studying them in a Brownian motion...

Pardoux and Peng (Systems Control Lett. 14 (1990) 55) introduced a class of nonlinear backward stochastic differential equations (BSDEs). According to Pardoux and Peng's theorem, the solution of this type of BSDE consists of a pair of adapted processes, say (y,z). Since then, many researchers...

This paper investigates the relationships between coherent (convex) risk measures and Choquet expectations under the g-expectations framework. We deduce that convex risk measures can be dominated by Choquet expectations if, and only if they are coherent risk measures.

In this paper, we get a general downcrossing inequality for g-martingales introduced via a class of backwards stochastic differential equations (shortly BSDEs).

Models of utility in stochastic continuous-time settings typically assume that beliefs are represented by a probability measure, hence ruling out a priori any concern with ambiguity. This paper formulates a continuous-time intertemporal version of multiple-priors utility, where aversion to...

An upper (lower) probability can be defined as a supremum (infimum) over a set of probability measures. The upper probability measure is also called a capacity. A capacity is usually studied under an assumption that it is 2-alternating, but many capacities are not 2-alternating. In this paper,...

Using the 2006 wave of the Chinese General Social Survey, the present paper examines the effect of risk attitudes on the likelihood of entrepreneurship in China. Our results show that risk attitudes have a nonlinear effect on the likelihood of being entrepreneurs. Risk neutral people are most...