3. Calculating Bernoulli’s Expected Value

To truly understand Safe Haven by Mark Spitznagel, you’ve got to do the math in it. Unfortunately, most people (me #1) aren’t very good at math. Because I want to understand Safe Haven, I’ll go through the math in these videos, and I’ll also share any questions/problems I have with Spitznagel’s explanations and math.

[hansay]

I also had hard time figuring out as there is no additional explanation as to using natural log. To tackle St. Petersburg paradox, Bernoulli took natural log as a form of utility function.
As the book explains, marginal utility theory was invented based upon this concept of utility function which indicates the value of stuff is dependent upon the amount held already. Utility function certainly doesn't have to be natural log, it may be square root or something.
What is really important is it seems Bernoulli, as he solved this paradox, had in mind that the key is geometric average as the natural log can be translated into one's ending capital after a series of gambling.

[williamwang]

This is late, but for natural log there are two conventions: the "ln" convention and the "log" convention. According to a college teaching assistant I had, "ln" is more a high school/Texas Instrument convention. For them, "log" has a default base of 10 and "ln" refers to the natural log. In college math and beyond, the default base for log is considered "e" (the natural log) and base 10 is explicitly labeled.

Since people don't always mention which convention, I always end up trying both base "e" and base 10 to see which one gets the right result.

[migerra]

Maybe ln is chosen to capture the non linearities in your gain (the utility). Imagine on x axis amount of dollar won and on y acis your utility and plot ln(x) on this. Then getting 1 dollar more when already having a lot of dollars does not grant you much utility (far end of x axis). While having almost no dollars getting 1 additional 1 dollar creates great deal of utility (beginning of x axis).

[asgunzi]

It is very common to use ln as log. But why log_e and not log10? In my view, the choice of basis is of little importance in this case. Much more important is to capture the essence of the idea: we have to have an order of magnitude of wealth to increase the utility. Someone with 10 million dollars will not be disturbed by losing or gaining 50 thousand.

[FirstLast-txyj]

How are you going to apply what you learn in this book to crypto?? He uses options and usually options are not present for shitcoins..