Continuoustime Growth

Optimal portfolio growth can be applied with any rebalancing period—a year, a month, a week, or a day. In the limit of very short time periods we consider continuous rebalancing.

In fact, there is a compelling reason to consider the limiting situation: the resulting equations for optimal strategies turn out to be much simpler, and as a consequence it is much easier to compute optimal solutions Hence even if rebalancing is to be carried out only, say, weekly, it is convenient to use the continuous-time formulation to do the calculations

The continuous-time version also provides important insight. For example, it reveals very clearly how volatility pumping works.

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