³¹We assume that $logψt+1$ and $logξt+1$ are normally distributed with means $2 - σψ∕2$ and $2 - σξ∕2$ and variances $σ2 ψ$ and $σ2 ξ$ (so that $M [ψ ]=M [ξ ]= 1 t+1 t+1$ ), where $M []$ is the mean operator defined below.