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This paper aims at a unified treatment of hedging in market models driven by martingales with deterministic bracket , including Brownian motion and the Poisson process as particular cases. Replicating hedging strategies for European, Asian and Lookback options are explicitly computed using either the Clark-Ocone formula or an extension of the delta hedging method, depending on which is most appropriate.
The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form:
, (1)
where is a set of admissible controls and is the solution of the following equation:
;
. (2).
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