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Based on utility theory, this paper firstly combined different utility functions with risk aversion coefficient and constructed different kinds of optimizing problems for hedgers to hedge for stochastic-payment-typed contingent claim, and then, by the aid of dynamic programming theory, effective multi-stage hedging strategy is proposed for different risk-averse hedgers. Lastly, the research results that the optimal hedging ratios for three kinds of utility functions are equivalent and do not relate to the risk aversion coefficient.

The Optimal Hedging Ratio for Contingent Claims Based on Different Risk Aversions