Example — Fair lottery and risk neutrality

When the lottery has zero mean, comparing it with a small certain gain highlights what a risk-neutral decision-maker does.

Example — When the lottery is fair, is the certain option preferable?

Variant: in the lottery I win $100$ EUR with prob. $1/2$ and lose $100$ EUR with prob. $1/2$. Then $\bar V_L = 0$ EUR. If the sure alternative pays even just $1$ EUR, it has a greater expected value. A risk-neutral rational agent always takes the certain option if the lottery has zero mean. (Casino bets have $\bar V_L<0$: the rational agent never plays.)

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Topics: Probability
Concepts: Risk aversion · Fair game · Expected value
Methods: Fair game
Skills: Probability calculation