First observe that the mappings Θ,¯¯¯¯Θ and M are all decreasing with respect to stochastic order, and continuous with respect to the topology of weak convergence. Note also that cˆf′(t)t=bf(t), so that
H′(t)=cf′(t)((f∘f)(t)−t). Thus, H′(t)=0 if and…