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We search for an optimal strategy to reduce the running risk inhedging a long-term commitment with short-term futures contracts underthe constraint of terminal risk.Suppose the market follows the simple stochastic differential equationdS,-μdt+σdB,,where Bt is the standard Brownian motion.The mathematicalmodel of the optimal problem can be expressed as follows.For a measurablefunction g o[0,1]n and ≤t≤1,defineF8(t)=∫0t(t-g(s))2ds.Under the condition F8(1),find the strategy function,if exists,which minimizes the running risk.We show that a unique solutionto the optimal problem always exists and provide analytic solutions undercertain conditions.