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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—Stendhal [Marie Henri Beyle] (1783–1842)
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—Henry David Thoreau (1817–1862)
“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)
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—George Bernard Shaw (1856–1950)