  Using elements from the theory of ergodic backward stochastic differential
equations (BSDE), we study the behavior of forward entropic risk measures. We
provide their general representation results (via both BSDE and convex duality)
and examine their behavior for risk positions of long maturities. We show that
forward entropic risk measures converge to some constant exponentially fast. We
also compare them with their classical counterparts and derive a parity result.
