论文标题
在长期以来的约束下，随机投资组合理论中强大的渐近生长
Robust Asymptotic Growth in Stochastic Portfolio Theory under Long-Only Constraints
论文作者
论文摘要
我们考虑在随机投资组合理论（SPT）中最大化投资者在漂移不确定性下的投资者的渐近增长率的问题。与Kardaras和Robertson的工作一样，我们将Markovian波动矩阵$ C（X）$和（II）的投入（i）作为市场重量的不变密度$ p（x）$，但我们还对投资者施加了长期以来的约束。我们的主要贡献证明了凹面功能生成的投资组合和开发有限尺寸近似的独特性和存在结果，可用于数值找到最佳。除了上面概述的一般结果外，我们还建议将一类广泛的模型用于挥发性矩阵$ c（x）$，可以将其校准到数据中，在其中，我们获得了任何不变密度的最佳无约束投资组合的显式公式。
We consider the problem of maximizing the asymptotic growth rate of an investor under drift uncertainty in the setting of stochastic portfolio theory (SPT). As in the work of Kardaras and Robertson we take as inputs (i) a Markovian volatility matrix $c(x)$ and (ii) an invariant density $p(x)$ for the market weights, but we additionally impose long-only constraints on the investor. Our principal contribution is proving a uniqueness and existence result for the class of concave functionally generated portfolios and developing a finite dimensional approximation, which can be used to numerically find the optimum. In addition to the general results outlined above, we propose the use of a broad class of models for the volatility matrix $c(x)$, which can be calibrated to data and, under which, we obtain explicit formulas of the optimal unconstrained portfolio for any invariant density.
