Here is Ole Peters: [Puzzle] “Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party’s wealth, whereas both parties must sign for such contracts to exist [Answer]: Time averages and expectation values differ because wealth changes are non-ergodic.”
Peters again: “Conceptually, its power derives from a new notion of rationality. Many reasonable models of wealth are non-stationary processes. Observables representing wealth then do not have the ergodic property of Section I, and therefore rationality must not be defined as maximizing expectation values of wealth. Rather, we propose as a null model to define rationality as maximizing the time-average growth of wealth.”
You write: “Kelly betting, on the other hand, assumes a finite bankroll—and indeed, might have to be abandoned or adjusted to handle negative money.” [Negative Interest rate?] Can you explain more? Would love to fit this conceptually into Peter’s Non-ergodic growth rate theory
Here is Ole Peters: [Puzzle] “Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party’s wealth, whereas both parties must sign for such contracts to exist [Answer]: Time averages and expectation values differ because wealth changes are non-ergodic.”
Peters again: “Conceptually, its power derives from a new notion of rationality. Many reasonable models of wealth are non-stationary processes. Observables representing wealth then do not have the ergodic property of Section I, and therefore rationality must not be defined as maximizing expectation values of wealth. Rather, we propose as a null model to define rationality as maximizing the time-average growth of wealth.”
You write: “Kelly betting, on the other hand, assumes a finite bankroll—and indeed, might have to be abandoned or adjusted to handle negative money.” [Negative Interest rate?] Can you explain more? Would love to fit this conceptually into Peter’s Non-ergodic growth rate theory