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In this article we investigate the occurrence of stock market crash in an economy cycle. Bayesian approach, Heston model and statistical–physical method are considered. Specifically, Heston model and an effective potential are employed to address the dynamic changes of stock price. Bayesian approach has been utilized to estimate the Heston model's unknown parameters. Statistical physical method is used to investigate the occurrence of stock market crash by calculating the mean time-limited crash rate. The real financial data from the Shanghai Composite Index is analyzed with the proposed methods. The mean time-limited crash rate of stock price is used to describe the occurrence of stock market crash in an economy cycle. The monotonous and nonmonotonous behaviors are observed in the behavior of the mean time-limited crash rate versus volatility of stock for various cross correlation coefficient between volatility and price. Also a minimum occurrence of stock market crash matching an optimal volatility is discovered. [ABSTRACT FROM AUTHOR]

The stability of portfolio investment in stock market crashes with Markowitz portfolio is investigated by the method of theoretical and empirical simulation. From numerical simulation of the mean escape time (MET), we conclude that: (i) The increasing number of stocks in Markowitz portfolio induces a maximum in the curve of MET versus the initial position; (ii) A critical value of in the behavior of MET versus the long-run variance or amplitude of volatility fluctuations maximumlly enhances the stability of portfolio investment. When takes value below the critical value, the increasing enhances the stability of portfolio investment, but restrains it when takes value above the critical value. In addition, a good agreement of both the MET and probability density functions of returns is found between real data and theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the trading time risk (TTR) of stock investment in the case of stock price drop of Dow Jones Industrial Average (ˆDJI) and Hushen300 data (CSI300), respectively. The escape time of stock price from the maximum to minimum in a data window length (DWL) is employed to measure the absolute TTR, the ratio of the escape time to data window length is defined as the relative TTR. Empirical probability density functions of the absolute and relative TTRs for the ˆDJI and CSI300 data evidence that (i) whenever the DWL increases, the absolute TTR increases, the relative TTR decreases otherwise; (ii) there is the monotonicity (or non-monotonicity) for the stability of the absolute (or relative) TTR; (iii) there is a peak distribution for shorter trading days and a two-peak distribution for longer trading days for the PDF of ratio; (iv) the trading days play an opposite role on the absolute (or relative) TTR and its stability between ˆDJI and CSI300 data. [ABSTRACT FROM AUTHOR]