On Asymptotic Log-Optimal Buy-and-Hold Strategy

In this paper, we consider a frequency-based portfolio optimization problem with $m \geq 2$ assets when the expected logarithmic growth (ELG) rate of wealth is used as performance metric. With aid notion called dominant asset, it known that optimal ELG level achieved by investing all available funds on asset. However, such an "all-in" strategy arguably too risky to implement in practice. Motivated issue, study case where weights are chosen rather ad-hoc manner and buy-and-hold subsequently used. Then show that, if underlying contains buy hold specific asset asymptotically log-optimal sublinear convergence. This result also extends scenario trader either does not have probabilistic model for returns or trust obtained from historical data. To be more specific, market involving nonzero each log-optimal. Additionally, paper includes conjecture regarding property high-frequency maximality. That is, absence transaction costs, rebalancing unbeatable sense. Support conjecture, lemma weak version provided. true, enables us improve log-optimality previously. Finally, indicates way issue about should one rebalance their needed, Examples, some simulations data, provided along illustrate the~theory.