Risk averse asymptotics and the optional decomposition

We consider the problem of maximizing expected utility for a general utility function on $\textbf R$ when the agent becomes increasingly risk averse. The limiting strategy will be shown to be a special, unique superhedging strategy, the so-called balanced strategy. The connections to the optional decomposition and the class of minimal hedging strategies described in [D. O. Kramkov, Probab. Theory Related Fields, 105 (1996), pp. 459–479] are examined.