The Risk Neutral Utility Function
Choice under uncertainty is often characterized as the maximization of expected utility. Utility is often assumed to be a function of profit or final portfolio wealth, with a positive first derivative. The utility function whose expected value is maximized is concave for a risk averse agent, convex for a risk lover, and linear for a risk neutral agent. Thus in the risk neutral case, expected utility of wealth is simply equal to a linear function of expected wealth, and maximizing it is equivalent to maximizing expected wealth itself.
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Famous quotes containing the words risk, neutral, utility and/or function:
“Men’s hearts are cold. They are indifferent. Not all the coal that is dug warms the world. It remains indifferent to the lives of those who risk their life and health down in the blackness of the earth; who crawl through dark, choking crevices with only a bit of lamp on their caps to light their silent way; whose backs are bent with toil, whose very bones ache, whose happiness is sleep, and whose peace is death.”
—Mother Jones (1830–1930)
“I feel the carousel starting slowly
And going faster and faster: desk, papers, books,
Photographs of friends, the window and the trees
Merging in one neutral band that surrounds
Me on all sides, everywhere I look.”
—John Ashbery (b. 1927)
“Moral sensibilities are nowadays at such cross-purposes that to one man a morality is proved by its utility, while to another its utility refutes it.”
—Friedrich Nietzsche (1844–1900)
“No one, however powerful and successful, can function as an adult if his parents are not satisfied with him.”
—Frank Pittman (20th century)