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Consider an option with maturity time T corresponding to a contingent claim H (in an incomplete market). A fair hedging price for H should take into account an optimal dynamical hedging plan against H. Let C t be the cumulative cost and ℑ t be the set of events of the history up to time t. You can choose the plan at time t such that you minimize (i) EC t +1 − C t 2 ∣ ℑ t, (ii) EC T − C t 2 ∣ ℑ t, or (iii) EC T − C 0 2. Sufficient conditions on the underlying stochastic process (in discrete time) are provided such that the fair hedging price does not depend on the choice of (i), (ii), or (iii), which fact should increase its acceptability.
Manfred Schäl (1994) studied this question.