is equal to the wealth that would have accrued to a $\$1$ deposit into the best rebalancing rule (or fixed-fraction betting scheme) determined in hindsight. Ordentlich and Cover (1998) began the work of pricing this option in the Black-Scholes (1973) market at time-$0$ for unlevered hindsight optimization over a single underlying risk asset. Garivaltis (2018) priced and replicated the rebalancing option at any time $t$ for levered hindsight optimization over an arbitrary number of correlated stocks in geometric Brownian motion. That paper obtained the elegant result that for completely relaxed (levered) hindsight optimization, the corresponding delta-hedging strategy simply looks back over the observed price history $[0,t]$, computes the best rebalancing rule in hindsight $b(S_t,t)$, and bets that fraction of wealth over the next differential time step $[t,t+dt]$.

The present paper studies Cover’s rebalancing option with hindsight optimization over a discrete set $\mathbb{B}:=\{b_1,...,b_n\}$ of rebalancing rules. Apart from the scientific obligation to extend Ordentlich and Cover’s incisive (1998) chain of reasoning, our approach has some interesting advantages relative to hindsight-optimization over all possible rebalancing rules. In our world, the (delta-hedging) practitioner is now free to express any of his institutional constraints or beliefs about future returns through a judicious choice of 