Los tres teoremas de Kenneth Boulding

Boulding's Three Theorems

These theorems are from the work of the eminent economist Kenneth Boulding (Boulding, 1971).

First Theorem: "The Dismal Theorem"

"If the only ultimate check on the growth of population is misery, then the population will grow until it is miserable enough to stop its growth."

Second Theorem: "The Utterly Dismal Theorem"

This theorem "states that any technical improvement can only relieve misery for a while, for so long as misery is the only check on population, the [technical] improvement will enable population to grow, and will soon enable more people to live in misery than before. The final result of technical] improvements, therefore, is to increase the equilibrium population which is to increase the total sum of human misery."

Third Theorem: "The moderately cheerful form of the Dismal Theorem" :

"Fortunately, it is not too difficult to restate the Dismal Theorem in' a moderately cheerful form, which states that if something else, other then misery and starvation, can be found which will keep a prosperous population in check, the population does not have to grow until it is miserable and starves, and it can be stably prosperous."

Boulding continues, "Until we know more, the Cheerful Theorem remains a question mark. Misery we know will do the trick. This is the only sure­fire automatic method of bringing population to an equilibrium'. Other things may do it."

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Volatility smile

In finance, the volatility smile is a long-observed pattern in which at-the-money options tend to have lower implied volatilities than other options. The pattern displays different characteristics for different markets, and is not well understood theoretically. In particular, American equity options did not show a volatility smile before the Crash of 1987 but began showing one afterwards.

A closely related concept is that of term structure of volatility, which refers to how implied volatility differs for related options with different maturities. An implied volatility surface is a 3-D plot that combines volatility smile and term structure of volatility into a consolidated view of all options for an underlier.

Source: Wikipedia