We consider the management of a mono-specific even-aged forest at the stand level. Optimal silviculture based on timber income and sequestered carbon income in an no risk case and a risky case are compared. In this study, using calculus of variations we discuss the validity of using a risk adjusted discount rate (a rate of natural risk added to the discount rate) or using a carbon adjusted discount rate (a rate of natural risk subtracted to the carbon discount rate) without risk to mimic the natural risk case in term of optimal thinnings. Except for very high risk rate values in the risky case, the optimal trajectory for carbon sequestration is very different from that obtained for the timber criterion. We show that without risk or with risk case but moderate risk rate, the optimal cutting age for sequestered carbon will be the senescence age. For higher risk rate the optimal cutting age for sequestered carbon may be more comparable to optimal timber cutting age.