Optimal Discrete Ratchet Consumption

Dybvig [1995] finds optimal spending and investment strategies for a perpetual endowment that has no tolerance for spending declines. His spending rule is a ratchet --- spending never decreases, but has a substantial chance of increasing. We find the ratchet consumption rule for an investor with a finite planning horizon. We maximize an expected utility that eschews pending declines, yet permits a range of choices for felicity and time preference functions. For optimality, a spending rule must be paired with an investment rule. Here, we investigate dynamic investment strategies --- we treat consumption as a derivative security and derive formulas for its delta-hedge