Abstract
Customizing the optimal derivative written on an “instrument” risk to hedge an exogenous pecuniary risk is only examined in a few works assuming specific objective function and/or distribution of the risks. We show that this problem is closely-related to a previously un-examined stochastic-solution problem which includes the constant-solution optimal hedge ratio problem as a degenerated case. We then suggest conditions on risks to range or explicitly solve for the stochastic solution. This updated perspective not only solves the optimal tailor-made hedge problem but also disentangles a popular missing inspection on the existence of solutions to many existing models.
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