The optimal time to buy and hold stock in a reversal
用最优停时理论构建了一个无序问题，研究下跌趋势即将反转时买入并持有股票的最佳时机，发现当回报反转的条件概率首次达到最优边界时应买入，该边界由股票回报、波动率和反转强度唯一决定。
Abstract Investors cannot anticipate a return reversal in the stock market. Therefore, choosing the optimal time to buy and hold a stock is vital. This paper formulates a disorder problem using the optimal stopping theory to study the optimal time to buy and hold a stock when a downward trend is about to reverse. The results show that investors should buy a stock when the conditional probability of a return reversal hits an optimal boundary for the first time. The optimal boundary is uniquely determined by the stock return, volatility, and the intensity of return reversal. Moreover, the optimal boundary decreases as the stock volatility and the intensity of return reversal increase. We use the China Securities Index 300 (CSI 300), Standard & Poor's 500 (S&P 500), Dow Jones Industrial Average (DJIA), and Russell 2000 indexes to estimate the parameters and the related optimal boundary. We find that the estimated optimal boundary can be used to time stock buying.