The Cover universal portfolio (UP from now on) has many interesting theoretical and numerical properties and was investigated for a long time. Building on it, we explore what happens when we add this UP to the market as a new synthetic asset and construct by recurrence higher order UPs. We investigate some important theoretical properties of the high order UPs and show in particular that they are indeed different from the Cover UP and are capable to break the time permutation invariance. Numerical experiences on a benchmark from the literature show that in all cases high order UPs improve Cover's UP performances.

翻译：Cover泛化投资组合（以下简称UP）具有众多引人关注的理论与数值特性，并已得到长期研究。在此基础上，我们探究将该UP作为新型合成资产纳入市场后，通过递推方式构建高阶UP时会发生的变化。我们研究了高阶UP的一些重要理论性质，特别证明了其确实异于Cover UP，且能够打破时间置换不变性。基于文献基准的数值实验表明，在所有情形下，高阶UP均能提升Cover UP的表现性能。