vNM function:

Theorem:

(vNM utility = expected utility)

Axioms:

The independence axiom:

• implies, order of preference between two lotteries 𝑝 and 𝑝′ is preserved if we combine the two lotteries with another lottery 𝑝′′.

• a small perturbation of two lotteries does not change the order of preferences

• assumption, however, is often not verified in real-life choices.

(eigene Erklärung): Since utility lines are parallel and increase to the right, and the connecting lines between L1 & L’1 and L2 & L’2 respectively, are also parallel, L1 is equally “better” than L’1 as L2  is than L’2

= global risk aversion measure

Und das ganze x(-1)

Other way around for convex of course

• Regret theory:

  • you do not only care about what you get money-wise, you also value the fact that you don’t want to be surprised after you made the choice

• Kahnemann & Tversky: indifference curves (utility lines) are not parallel, they rotate around a fixed point

• Rank dependent expected utility (weighted probability):

1. Rank outcomes in terms of utility

2. apply probability weighting function W=[0,1]->[0,1]

—> re-weighting true probability

—> overweights unlikely events

(=higher returns)

Wikipedia:

Random variable A has first-order stochastic dominance over random variable B if for any outcome x, A gives at least as high a probability of receiving at least x as does B, and for some x, A gives a higher probability of receiving at least x.

G is a mean-preserving spread of F

CE = amount of money, that makes an individual indifferent between holding that amount of money or the lottery

RP = E(L)-CE

compensation; what I need in addition to CE to play the lottery