Before revision:  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  .
After revision:  We introduce a sequence of new financial instruments best suited for hedging in jump-diffusion and stochastic volatility market models . The new instruments we introduce are perpetual derivatives. More specifically, they are options with perpetual maturities. In a financial market where perpetual derivatives are introduced, there is a new set of partial and partial and partial-integro differential equations for pricing derivatives .