Monday, November 8, 2010

Convex function vs Concave function

Nassim Taleb's staircase is a very good model for describing life. If life could be treated as a function then it should be a convex function which is not smooth.

Definition of a convex function:

  • A function which always gains more than it loses
The function shown in the image is an example of a concave function. Life is generally a staircase, where there is relative stability for extended periods of time followed by a jump or a fall. When modeling or making decisions in one's life, one must always insure that the fall should be lesser than the rise. People taking too much downside risk would represent the concave function shown above. The fall should always be lesser. 

Investments (time, work, capital) should be made in opportunities that have enormous upsides where as the downside must be insured. For example, when starting a business, make sure that you have something to fall back on if the promised business plan never materializes. Start your first business without taking too much risk, preferably while working and only quitting once the business generates the positive results. 

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