We investigate a portfolio optimization problem under the threat of a market crash, where the interest rate of the bond is modeled as a Vasicek process, which is correlated with the stock price process. We adopt a non-probabilistic worst-case approach for the height and time of the market crash. On a given time horizon [0, T ], we then maximize the investor’s expected utility of terminal wealth...

Modern day stock markets have almost entirely became automated. Even though it means increased profits for the investors by algorithms acting upon the slightest price change in order of microseconds, it also has given birth to many ethical dilemmas in the sense that slightest mistake can cause people to lose all of their livelihoods. This paper reviews one such event that happened on May 06, 20...

We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize the importance of feedback effects of price variations onto themselves. Risk aversion, in particular, leads to an ‘up-down’ symmetry breaking te...

This paper provides direct evidence of leverage-induced re sales leading to a major stock market crash. Our analysis uses proprietary account-level trading data for brokerageand shadownanced margin accounts during the Chinese stock market crash in the summer of 2015. We nd that margin investors heavily sell their holdings when their account-level leverage edges toward their maximum leverage lim...