We develop a new method for hedging derivatives based on the premise that a hedger should not always rely on a universal set of trading instruments that are used to form a linear portfolio of the stock, riskless bond and standard derivatives, but rather should design a set of specific, most suited financial instruments for the hedging problem. We introduce a sequence of new financial instruments best suited for hedging in jump-diffusion and stochastic volatility market models and those with long-range dependence. Our methods lead to a new set of partial and partial and partial-integro differential equations for pricing derivatives.
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