The safety equivalent is a term from the decision theory. It designates that safe value and/or money, with which a Entscheider, which possesses a Lotterie L, is indifferent, this to keep or deliver.

Formal description

L is a Lotterie with the consequence quantity x_i and the pertinent probabilities p_i. The moreover one u are a constant use function, with the inverse function u^ {- 1}, and x a safe output ability of a Entscheiders. The equation

u (x+s*) = E (u (x+L))

it describes that the use safety equivalent equal to the expectancy value of the use of the Lotterie L is. Thus the Entscheider is indifferent between the uncertain Lotterie and the safety equivalent. Transformed arises therefore for s* the following equation

s* = u^ {- 1} (E (u (x+L)))- x.

For risikoaverse Entscheider the safety equivalent is strictly smaller than the expectancy value of the Lotterie. A risikoaverser Entscheider is thus ready, a Lotterie L, which he possesses, to a smaller amount than delivering the expectancy value. The amount of difference between safety equivalent and the expectancy value of the Lotterie is called risk premium.

With risk-joyful Entscheider the safety equivalent is strictly more largely than the expectancy value of the Lotterie during with risk-neutral Entscheidern safety equivalent and expectancy value of the Lotterie corresponds itself.

Articles in category "Safety equivalent"

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