در برابر ثبات همزمان معاملات کوتاه مدت معاملات سهام با تغییر زمان قیمت دینامیک

This paper provides a time-varying extension of the so-called Robust Positive Expectation Theorem which arises in the context of Simultaneous Long-Short (SLS) stock trading. In the literature, the original version of the theorem applies to an idealized market with prices governed by a constant-parameter Geometric Brownian Motion (GBM). By this we mean that the process drift µ and voltility σ are time-invariant. In this context, the SLS strategy leads to the guarantee of a positive expected trading gain at every instant of time. In this paper, this result is generalized to GBM price dynamics with these two parameters allowed to be continuously time-varying with no restrictions on their rate of change. The motivation for considering this more general class of stock-price variations is the following: At first glance, it appears that these time-varying price dynamics are “unbeatable” in the sense that there cannot be a stock-trading strategy which still leads to robust positive expectation. In this regard, the “surprising” result in this paper is that the same SLS controller used in the time-invariant case also works in the time-varying case. These results strengthen the case made in earlier literature that linear feedback control in stock trading is worthy of further research.