1/3
In 2011 I gave a TEDx talk and had to illustrate ergodicity breaking somehow.
I chose a coin toss. Heads: wealth x is multiplied by 1.5; tails: by 0.6.
I liked the memorable symmetry. Expectation goes up, reality goes down. Both at ~5% per round.
In 2011 I gave a TEDx talk and had to illustrate ergodicity breaking somehow.
I chose a coin toss. Heads: wealth x is multiplied by 1.5; tails: by 0.6.
I liked the memorable symmetry. Expectation goes up, reality goes down. Both at ~5% per round.
2/3 Some comments
a) This game is nothing but geometric Brownian motion, as one might implement it on a computer (i.e. discretized). It's the workhorse model of mathematical finance.
b) There's nothing special about 0.6 and 1.5. For example 1.3 and 1.7 would work just as well.
a) This game is nothing but geometric Brownian motion, as one might implement it on a computer (i.e. discretized). It's the workhorse model of mathematical finance.
b) There's nothing special about 0.6 and 1.5. For example 1.3 and 1.7 would work just as well.
3/3
c) Following from b), this is not about ruin or bankruptcy. No one can "go bankrupt" in this game because x=0 is inaccessible. You can add some solvency criterion "if you have less than $1, I consider you bankrupt" but that's add-on structure. It's not the key point.
c) Following from b), this is not about ruin or bankruptcy. No one can "go bankrupt" in this game because x=0 is inaccessible. You can add some solvency criterion "if you have less than $1, I consider you bankrupt" but that's add-on structure. It's not the key point.
