The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density f(x)~f_0 x^(-2), with the coefficient depending on the means and variances of the numerator and denominator, and their correlation. We also obtain the conditional...

Stocks are one of the aspects that affect the economy in the world. In the stock market, the price of a stock changes every time. Investors who are able to predict the increase in stock prices will tend to get profit, but investors who are unable to predict the increase in stock prices will tend...

We perform a large simulation study to examine the extent to which various generalized autoregressive conditional heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 stock market returns ranging from 1995-2014...