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Option hedging for semimartingales


  • Schweizer, Martin


We consider a general stochastic model of frictionless continuous trading. The price process is a semimartingale and the model is incomplete. Our objective is to hedge contingent claims by using trading strategies with a small riskiness. To this end, we introduce a notion of local R-minimality and show its equivalence to a new kind of stochastic optimality equation. This equation is solved by a Girsanov transformation to a minimal equivalent martingale measure. We prove existence and uniqueness of the solution, and we provide several examples. Our approach contains previous treatments of option trading as special cases.

Suggested Citation

  • Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
  • Handle: RePEc:eee:spapps:v:37:y:1991:i:2:p:339-363

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