[NOTE: Text or symbols not renderable in plain text are indicated by [...]. See PDF document for full abstract.] In this dissertation, we search for an optimal strategy to reduce the running risk in hedging a long-term supply commitment with short-term futures contracts under a certain constraint on the terminal risk, which leads to a class of intrinsic optimization problems. Motivated by a simple model initially discussed in [1] Culp and Miller, [8] Mello and Parsons, [4] Glasserman and a best strategy model by [5] Larcher and Leobacher, we studied an optimization problem as following: Under the condition that [...] Which measurable function [...] minimizes the value of [...]? We will show that a unique solution to this general problem always exists. By solving it numerically, we obtain a general dynamic solution. Furthermore, we will discuss properties of the solution and give analytic solutions in some special cases.