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Option hedging for semimartingales

Martin Schweizer

Stochastic Processes and their Applications, 1991, vol. 37, issue 2, 339-363

Abstract: 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.

Keywords: option; hedging; semimartingales; R-minimality; optimality; equation; minimal; martingale; measure; continuous; trading; Black-Scholes; model; contingent; claims; incomplete; markets (search for similar items in EconPapers)
Date: 1991
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