Uncertainty and Probability Continuous Time: g–expectations

Time–consistent multiple priors are g–expectations

g–expectations

Conditionalg–expectation of anFT–measurable random variableX

at timetisEt(X) :=Yt

where (Y,Z) solves the backward stochastic differential equation

YT=X, ,−dYt=g(t,Yt,Zt)−ZtdWt

the probability theory forg–expectations has been mainly developed

by Shige Peng

Theorem (Delbaen, Peng, Rosazza Giannin)

“All” time–consistent multiple prior expectations are g –expectations.