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The paper deals with the problem of finding an optimal one-time rebalancing strategy assuming that in the Black–Scholes model the drift term of the stock may change its value spontaneously at some random non-observable (hidden) time. The problem is studied on a finite time interval under two criteria of optimality (logarithmic and linear). The methods of the paper are based on the results for the quickest detection of drift change for Brownian motion.

On a stochastic version of the trading rule “Buy and Hold”