There is a fundamental link between Lognormal Cascade Distribution and Double Pareto Distribution. But I have not been able to make a good sense out of them.

Double Pareto is not only a stable solution of Komogorov diffusion equation, it is also a extreme case of the ground state of a quantum well (when the width of well is zero). So a Double Pareto distribution (or Lognormal Cascade) implies the underlying population is in a confined state, which brings me to think about Financial Cycles.

An interesting book to read is the Income Distribution of D. G. Champernowne. It enlightened me to think outside of just quantitative finance - stuff that makes money. The fact that the world operates based on random growth is quite scary. Such economic system is fundamentally volatile and will bring about eqconomic inequality no matter what. Billionaires and political strongmen are just a product of such random growth system.

So you should understand that it is very understandable that Dow rose 10 times - from 1000 to 10000 - in 20 years, and it could go nowhere for another 20 years. That is just part of life. Treasury will do the same. Inflation, gold, commodity will behave similarly.

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