The Theory of Higher Order Lognormal Cascade Distribution and the Origin of Fat Tails in the Fluctuations of Stock Market

On the Network Effect in the Stock Market, The N^3/2 Power Law, and Optimal Volatility Equilibrium

“…Thus the Mean Reversion of Market Volatility is a natural outcome of Optimal Volatility Equilibrium. Lognormal Cascade Distribution: If 1 2 ψ(t) is normally distributed with variance η 2 , then the log-return of the market value process Z(t) follows a first-order symmetric lognormal cascade distribution (Lihn 2009…”

Comment on P. K. Clark's Distribution of Lognormal-Normal Increments and the Lognormal Cascade Distribution

“…In page 12 of P. K. Clark's 1973 paper, Theorem (5) proposed that a random process subordinated to a normal process with independent increments distributed N (0, σ 2 2 ) and directed by a lognormal with independent increments (and parameters µ and σ 2 1 ) has the 1 following lognormal-normal increments:…”

“…I have been studying the so-called Lognormal Cascade Distribution (Lihn, 2008(Lihn, , 2009(Lihn, , 2010. This distribution can be derived as the aggregate log-return distribution of a market consisting a group of stocks (Lihn 2009).…”