具有离散后见之明优化的盖的再平衡选项
Cover's Rebalancing Option With Discrete Hindsight Optimization
摘要：
我们研究T. Cover的再平衡选择（Ordentlich and Cover 1998）在连续时间离散后见之明优化下。我们所讨论的回报等于最终财富，它是将$\$1$存入事后确定的某个有限（也许是有限）再平衡规则集合中的最佳规则而积累起来的。再平衡规则（或固定比例投注方案）相当于固定资产配置（即$200\%$股票和$-100\%$债券），然后持续执行再平衡交易以抵消配置漂移。将后见之明的优化限制在少量的再平衡规则（即2）上，比Cover $\&$公司在其关于通用投资组合的辉煌理论（1986，1991，1996，1998）中所采取的开创性方法有一些优势，在该理论中，一个人的在线交易表现是相对于后见之明的任何类型的最佳无杠杆再平衡规则的最终财富来基准的。我们的方法让从业者表达一个先验的观点，即一个受青睐的资产配置（“赌注”）$b\in\{b_1,...,b_n\}$将在事后证明表现非常好。在将我们的鲁棒性限制在一些离散的资产配置集合（而不是所有可能的资产配置）时，我们降低了再平衡选项的价格，并保证在规划期结束时实现相应更高比例的后见之明优化财富。一个从业者谁的生活三角洲对冲这种变体的封面的再平衡选择通过几十年来保证看到的一天，他实现的复合年资本增长率是非常接近的最好的$b_i$事后。因此，最低点的期权价格。
英文摘要：
We study T. Cover's rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $\$1$ deposit into the best of some finite set of (perhaps levered) rebalancing rules determined in hindsight. A rebalancing rule (or fixed-fraction betting scheme) amounts to fixing an asset allocation (i.e. $200\%$ stocks and $-100\%$ bonds) and then continuously executing rebalancing trades to counteract allocation drift. Restricting the hindsight optimization to a small number of rebalancing rules (i.e. 2) has some advantages over the pioneering approach taken by Cover $\&$ Company in their brilliant theory of universal portfolios (1986, 1991, 1996, 1998), where one's on-line trading performance is benchmarked relative to the final wealth of the best unlevered rebalancing rule of any kind in hindsight. Our approach lets practitioners express an a priori view that one of the favored asset allocations ("bets") $b\in\{b_1,...,b_n\}$ will turn out to have performed spectacularly well in hindsight. In limiting our robustness to some discrete set of asset allocations (rather than all possible asset allocations) we reduce the price of the rebalancing option and guarantee to achieve a correspondingly higher percentage of the hindsight-optimized wealth at the end of the planning period. A practitioner who lives to delta-hedge this variant of Cover's rebalancing option through several decades is guaranteed to see the day that his realized compound-annual capital growth rate is very close to that of the best $b_i$ in hindsight. Hence the point of the rock-bottom option price.
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