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For a large class of vanilla contingent claims, we establish an explicitF\"ollmer-Schweizer decomposition when the underlying is a process withindependent increments (PII) and an exponential of a PII process. This allowsto provide an efficient algorithm for solving the mean variance hedgingproblem. Applications to models derived from the electricity market areperformed.

Variance Optimal Hedging for continuous time processes with independent increments and applications