Option hedging for semimartingales
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.
Year of publication: |
1991
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Authors: | Schweizer, Martin |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 37.1991, 2, p. 339-363
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Publisher: |
Elsevier |
Keywords: | option hedging semimartingales R-minimality optimality equation minimal martingale measure continuous trading Black-Scholes model contingent claims incomplete markets |
Saved in:
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